Geometry of 6-Dimensional Hermitian Manifolds of the Octave Algebra
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  • 作者:M. B. Banaru
  • 刊名:Journal of Mathematical Sciences
  • 出版年:2015
  • 出版时间:June 2015
  • 年:2015
  • 卷:207
  • 期:3
  • 页码:354-388
  • 全文大小:376 KB
  • 参考文献:1.A. Abu-Saleem, 鈥淪ome remarks on almost Hermitian manifolds with J-invariant Ricci tensor,鈥?Int. Math. Forum, 5, No. 2 (2010).
    2.A. Abu-Saleem and M. Banaru, 鈥淪ome applications of Kirichenko tensors,鈥?An. Univ. Oradea, Fasc. Mat., 17, No. 2, 201鈥?08 (2010).MATH MathSciNet
    3.O. E. Arsen鈥檈va and V. F. Kirichenko, 鈥淪elf-dual geometry of generalized Hermitian surfaces,鈥?Mat. Sb., 189, No. 1, 21鈥?4 (1998).MATH MathSciNet
    4.M. B. Banaru, A new characterization of the classes of almost Hermitian Gray鈥揌ervella structures [in Russian], preprint, Smolensk. State Pedagogical Institute (1992). Deposited at the All-Russian Institute for Scientific and Technical Information (VINITI), Moscow, No. 3334-B92.
    5.M. B. Banaru, 鈥淕ray鈥揌ervella classes of almost Hermitian structures on 6-dimensional submanifolds of Cayley algebras,鈥?in: Proc. Int. Mat. Conf. Dedicated to the 200th Anniversary of N. I. Lobachevskii, Akad. Nauk Resp. Belarus鈥?/em>, 1, Minsk (1993), p. 40.
    6.M. B. Banaru, On the Gray鈥揌ervella classification of almost Hermitian structures on 6-dimensional submanifolds of Cayley algebras [in Russian], Smolensk. State Pedagogical Institute (1993). Deposited at the All-Russian Institute for Scientific and Technical Information (VINITI), Moscow, No. 118-B93.
    7.M. B. Banaru, On almost Hermitian structures induced by 3-vector products on 6-dimensional submanifolds of Cayley algebras [in Russian], Smolensk. State Pedagogical Institute (1993). Deposited at the All-Russian Institute for Scientific and Technical Information (VINITI), Moscow, No. 1282-B93.
    8.M. B. Banaru, 鈥淥n the minimality of almost Hermitian 6-dimensional submanifolds of Cayley algebras,鈥?in Proc. Int. Sci. Conf. 鈥淧ontryagin Readings鈥揑V,鈥?/em> Voronezh (1993), p. 17.
    9.M. B. Banaru, 鈥淥n the para-K盲hlerian property of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Differential Geometry of Manifolds of Figures [in Russian], 25, Kaliningrad State Univ., Kaliningrad (1994), pp. 15鈥?8.
    10.M. B. Banaru, 鈥淥n the para-K盲hlerian property of six-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Webs and Quasigroups [in Russian], Kalinin, (1994), pp. 81鈥?3.
    11.M. B. Banaru, 鈥淕ray鈥揌ervella classes of almost Hermitian structures on 6-dimensional submanifolds of Cayley algebras,鈥?in: Proc. Moscow State Pedagogical Univ., Moscow (1994), pp. 36鈥?8.
    12.M. B. Banaru, 鈥淥n the holomorphic bisectional curvature of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Differential Geometry of Manifolds of Figures [in Russian], 28, Kaliningrad State Univ., Kaliningrad (1997), pp. 7鈥?.
    13.M. B. Banaru, 鈥淥n almost Hermitian structures induced by 3-vector products on 6-dimensional submanifolds of the octave algebra,鈥?in: Polyanalytic Functions: Boundary Properties and Boundary-Value Problems [in Russian], Smolensk (1997), pp. 113鈥?17.
    14.M. B. Banaru, 鈥淥n the properties of the curvature of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Proc. Int. Semin. 鈥淪elected Questions of Higher Mathematics and Informatics鈥?/em>, Smolensk (1997), pp. 25鈥?6.
    15.M. B. Banaru, 鈥淥n spectra of the most important tensors of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: The Newest Problems of the Field Theory [in Russian], Kazan鈥?(2000), pp. 18鈥?2.
    16.M. B. Banaru, 鈥淥n 6-dimensional submanifolds of Cayley algebras,鈥?in: Differential Geometry of Manifolds of Figures [in Russian], 31, Kaliningrad State Univ., Kaliningrad (2000), pp. 6鈥?.
    17.M. B. Banaru, 鈥淥n 6-dimensional G 1-submanifolds of the octave algebra,鈥?in: Proc. Moscow State Pedagogical Univ., Moscow (2000), pp. 165鈥?71.
    18.M. B. Banaru, 鈥淎 note on six-dimensional Vaisman鈥揋ray submanifolds of Cayley algebras,鈥?in: Webs and Quasigroups [in Russian], Tver (2000), pp. 139鈥?42.
    19.M. B. Banaru, 鈥淎 note on six-dimensional Hermitian submanifolds of Cayley algebras,鈥?Bul. S赂tiint赂. Univ. Politeh. Timi赂s., 45(59), No. 2, 17鈥?0 (2000).
    20.M. B. Banaru, 鈥淪ix theorems on six-dimensional Hermitian submanifolds of Cayley algebras,鈥?Izv. Akad. Nauk Resp. Moldova. Ser. Mat., 3 (34), 3鈥?0 (2000).
    21.M. B. Banaru, 鈥淥n six-dimensional Hermitian submanifolds of Cayley algebras satisfying the g-cosymplectic hypersurfaces axiom,鈥?Ann. Univ. Sofia Fac. Math. Inform., 94, 91鈥?6 (2000).MathSciNet
    22.M. B. Banaru, 鈥淥n 6-dimensional W 4-submanifolds of the octave algebra,鈥?in: Proc. Moscow State Pedagogical Univ., Moscow (2001), pp. 46鈥?8.
    23.M. B. Banaru, 鈥淎 new example of an R 2-manifold,鈥?in: Proc. VIII Int. Sci. Conf. 鈥淢athematics. Computer. Education,鈥?/em> Moscow (2001), p. 125.
    24.M. B. Banaru, 鈥淥n conformally flat c-para-K盲hlerian manifolds,鈥?in: Proc. IX Int. Conf. 鈥淢athematica. Education. Economics. Ecology,鈥?/em> Cheboksary (2001), p. 35.
    25.M. B. Banaru, 鈥淥n R 2- and cR 2-manifolds,鈥?in: Mathematics. Computer. Education [in Russian], 8, Moscow (2001), pp. 471鈥?76.
    26.M. B. Banaru, 鈥淥n locally Euclidean para-K盲hlerian manifolds,鈥?in: Proc. Ukrain. Math. Congr., Kiev (2001), pp. 13鈥?4.
    27.M. B. Banaru, 鈥淥n AH-manifolds with J-invariant Ricci tensor,鈥?in: Proc. IV Int. Conf. on Geometry and Topology, Cherkassy (2001), p. 9.
    28.M. B. Banaru, 鈥淥n para-K盲hlerian and c-para-K盲hlerian manifolds,鈥?in: Differential Geometry of Manifolds of Figures [in Russian], 32, Kaliningrad State Univ., Kaliningrad (2001), pp. 8鈥?3.
    29.M. B. Banaru, 鈥淥n the geometry of cosymplectic hyperplanes of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Proc. Int. Sci. Conf. 鈥淰olga-2001鈥?(Petrovskii Readings), Kazan鈥?(2001), p. 25.
    30.M. B. Banaru, 鈥淥n the Einstein property of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Studies in the Boundary-Value Problems of Complex Analysis and Differential Equations [in Russian], 3, Smolensk (2001), pp. 28鈥?5.
    31.M. B. Banaru, 鈥淥n the geometry of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Invariant Methods of the Study of Structures on Manifolds in Geometry, Analysis, and Mathematical Physics [in Russian] (L. E. Evtushik and A. K. Rybnikov, eds.), 1, Moscow (2001), pp. 16鈥?0.
    32.M. B. Banaru, 鈥淥n six-dimensional Hermitian submanifolds of Cayley algebras,鈥?Stud. Univ. Babe艧-Bolyai. Math., 46, No. 1, 11鈥?4 (2001).MATH MathSciNet
    33.M. B. Banaru, 鈥淭wo theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebras,鈥?J. Harbin Inst. Tech., 8, No. 1, 38鈥?0 (2001).
    34.M. B. Banaru, 鈥淎 note on Kirichenko tensors,鈥?in: Proc. Int. Sci. Conf. 鈥淰olga-2001鈥?(Petrovskii Readings), Kazan鈥?(2001), p. 26.
    35.M. B. Banaru, 鈥淎 new characterization of the Gray鈥擧ervella classes of almost Hermitian manifolds,鈥?in: Proc. 8th Int. Conf. on Differential Geometry and Its Aplications, Opava, Czech Republic (2001), p. 4.
    36.M. B. Banaru, 鈥淎 note on RK- and CRK-manifolds,鈥?Izv. Akad. Nauk Resp. Moldova. Ser. Mat., 1 (35), 37鈥?3 (2001).MathSciNet
    37.M. B. Banaru, 鈥淥n six-dimensional G1-submanifolds of Cayley algebras,鈥?Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 40, 17鈥?1 (2001).MATH MathSciNet
    38.M. B. Banaru, 鈥淥n the holomorphic bisectional curvature of six-dimensional Hermitian submanifolds of Cayley algebras,鈥?Bull. Transilv. Univ. Bra艧ov., 8 (43), 19鈥?3 (2001).MathSciNet
    39.M. B. Banaru, 鈥淭wo theorems on cosymplectic hypersurfaces of six-dimensional K盲hlerian submanifolds of Cayley algebras,鈥?Bul. 艦tiint赂. Univ. Politeh. Timi艧., 46, No. 2, 13鈥?7 (2001).MathSciNet
    40.M. B. Banaru, 鈥淎 note on almost Hermitian manifolds with a J-invariant Ricci tensor,鈥?Izv. Akad. Nauk Resp. Moldova. Ser. Mat., 3 (37), 88鈥?2 (2001).MathSciNet
    41.M. B. Banaru, 鈥淪ome theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebras,鈥?Mat. Vesn. (Bull. Math. Soc. Serbia), 53, Nos. 3-4, 103鈥?10 (2001).MATH MathSciNet
    42.M. B. Banaru, 鈥淎 note on six-dimensional G 2-submanifolds of Cayley algebras,鈥?An. 艦tiint赂. Univ. Al. I. Cuza. Ia艧i. Mat., 47, No. 2, 389鈥?96 (2001).MATH MathSciNet
    43.M. B. Banaru, 鈥淥n the typical number of symmetric 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?Proc. IX Int. Sci. Conf. 鈥淢athematics. Computer. Education,鈥?/em>, Moscow (2002), pp. 118.
    44.M. B. Banaru, 鈥淥n W 3-manifolds satisfying the axiom of G-cosymplectic hypersurfaces,鈥?Proc. XXIV Conf. Young Scientists, Moscow State Univ., Moscow (2002), pp. 15鈥?9.
    45.M. B. Banaru, 鈥淭wo theorems on cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?Izv. Vyssh. Uchebn. Zaved. Ser. Mat., 1 (476), 9鈥?2 (2002).MathSciNet
    46.M. B. Banaru, 鈥淥n the typical number of planar 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Problems of Theor. Cybernetics. Proc. XIII Int. Conf. (O. B. Lupanov, ed.), 1, Moscow (2002), pp. 19.
    47.M. B. Banaru, 鈥淗ermitian geometry of 6-dimensional submanifolds of Cayley algebras,鈥?Mat. Sb., 193, No. 5, 3鈥?6 (2002).MathSciNet
    48.M. B. Banaru, 鈥淥n the semi-K盲hlerian property of 6-dimensional almost Hermitian submanifolds of the octave algebra,鈥?Proc. Int. Sci. Conf. 鈥淰olga-2002鈥?(Petrovskii Reaings), Kazan鈥?(2002), pp. 15.
    49.M. B. Banaru, 鈥淥n spectra of some tensors of six-dimensional K盲hlerian submanifolds of Cayley algebras,鈥?Stud. Univ. Babe艧-Bolyai. Math., 47, No. 1, 11鈥?7 (2002).MATH MathSciNet
    50.M. B. Banaru, 鈥淥n Kenmotsu hypersurfaces in a six-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Proc. Int. Conf. 鈥淐ontemporary Geometry and Related Topics,鈥?/em> Beograd (2002), p. 5.
    51.M. B. Banaru, 鈥淎 note on R 2- and CR 2-manifolds,鈥?J. Harbin Inst. Tech., 9, No. 2, 136鈥?38 (2002).MATH
    52.M. B. Banaru, 鈥淎 note on six-dimensional G1-submanifolds of the octave algebra,鈥?Taiwanese J. Math., 6, No. 3, 383鈥?88 (2002).MATH MathSciNet
    53.M. B. Banaru, 鈥淪ix-dimensional Hermitian submanifolds of Cayley algebras and u-Sasakian hypersurfaces axiom,鈥?Izv. Akad. Nauk Resp. Moldova. Ser. Mat., 2 (39), 71鈥?6 (2002).MathSciNet
    54.M. B. Banaru, 鈥淥n totally umbilical cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebras,鈥?Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 41, 7鈥?2 (2002).MATH MathSciNet
    55.M. B. Banaru, 鈥淪ome remarks on para-K盲hlerian and C-para-K盲hlerian manifolds,鈥?Bull. Transilv. Univ. Bra艧ov., 9 (44), 11鈥?8 (2002).MathSciNet
    56.M. B. Banaru, 鈥淥n the type number of six-dimensional planar Hermitian submanifolds of Cayley algebras,鈥?Kyungpook Math. J., 43, No. 1, 27鈥?5 (2003).MATH MathSciNet
    57.M. B. Banaru, 鈥淎 note on para-K盲hlerian manifolds,鈥?Kyungpook Math. J., 43, No. 1, 49鈥?1 (2003).MATH MathSciNet
    58.M. B. Banaru, 鈥淎 note on Kirichenko tensors,鈥?in: The Newest Problems of the Field Theory [in Russian], Kazan鈥?(2003), pp. 56鈥?2.
    59.M. B. Banaru, 鈥淥n cosymplectic hypersurfaces of 6-dimensional K盲hlerian submanifolds of Cayley algebras,鈥?Izv. Vyssh. Uchebn. Zaved. Ser. Mat., 7 (494), 59鈥?3 (2003).MathSciNet
    60.M. B. Banaru, 鈥淥n the geometry of cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: The Newest Problems of the Field Theory [in Russian], Kazan鈥?(2003), pp. 38鈥?3.
    61.M. B. Banaru, 鈥淥n the eight Gray鈥揌ervella classes of almost Hermitian structures realized on 6-dimensional submanifolds of Cayley algebras,鈥?The Newest Problems of the Field Theory [in Russian], Kazan鈥?(2003), pp. 44鈥?0.
    62.M. B. Banaru, 鈥淥n 6-dimensional G 2-submanifolds of Cayley algebras,鈥?Mat. Zametki, 74, No. 3, 323鈥?28 (2003).MathSciNet
    63.M. B. Banaru, 鈥淥n an hypersurfaces of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?Mat. Sb., 194, No. 8, 13鈥?4 (2003).MathSciNet
    64.M. B. Banaru, 鈥淥n the typical number of cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?Sib. Mat. Zh., 44, No. 5, 981鈥?91 (2003).MATH MathSciNet
    65.M. B. Banaru, 鈥淥n Kenmotsu hypersurfaces of 6-dimensional Hermitian submanifolds of Cayley algebras,鈥?in: Differential Geometry of Manifolds of Figures [in Russian], 34, Kaliningrad State Univ., Kaliningrad (2003), pp. 12鈥?1.
    66.M. B. Banaru, 鈥淥n Kenmotsu hypersurfaces in a six-dimensional Hermitian submanifold of Cayley algebras,鈥?Proc. of the Workshop 鈥淐ontemporary Geometry and Related Topics,鈥?Belgrade, Yugoslavia May 15鈥?1, 2002, World Scientific, Singapore (2004), pp. 33鈥?0.
    67.M. B. Banaru, 鈥淥n the Gray鈥揌ervella classes of AH-structures on six-dimensional submanifolds of Cayley algebras,鈥?Ann. Univ. Sofia Fac. Math. Inform., 95, 125鈥?31 (2004).MATH MathSciNet
    68.M. B. Banaru, 鈥淥n some almost contact metric hypersurfaces in six-dimensional special Hermitian submanifolds of Cayley algebras,鈥?Proc. Int. Conf. 鈥淪elected Questions of Contemporary Mathematics鈥?Dedicated to the 200th Anniversary of C. Jacobi, Kaliningrad (2005), pp. 6.
    69.M. B. Banaru, 鈥淣ew results of the geometry of almost K盲hlerian manifolds,鈥?in: Proc. XV Military-Scientific Conf., 4, Smolensk (2007), pp. 88鈥?0.
    70.M. Banaru and G. Banaru, 鈥淥n six-dimensional planar Hermitian submanifolds of Cayley algebras,鈥?Bul. 艦tiint赂. Univ. Politeh. Timi艧., 46 (60), No. 1, 13鈥?7 (2001).
    71.M. B. Banaru and V. F. Kirichenko, 鈥淗ermitian geometry of 6-dimensional submanifolds of Cayley algebras,鈥?Usp. Mat. Nauk, 49, No. 1, 205鈥?06 (1994).MathSciNet
    72.F. Belgun and A. Moroianu, 鈥淣early K盲hler 6-manifolds with reduced holonomy,鈥?Ann. Global Anal. Geom., 19, 307鈥?19 (2001).MATH MathSciNet
    73.A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin (1987).MATH
    74.R. Brown and A. Gray, 鈥淰ector cross products,鈥?Comment. Math. Helv., 42, 222鈥?36 (1967).MATH MathSciNet
    75.R. L. Bryant, 鈥淪ubmanifolds and special structures on the octonions,鈥?J. Differ. Geom., 17, 185鈥?32 (1982).MATH
    76.E. Calabi, 鈥淐onstruction and properties of some 6-dimensional almost complex manifolds,鈥?Trans. Am. Math. Soc., 87, No. 2, 407鈥?38 (1958).MATH MathSciNet
    77.麓E. Cartan, Le赂cons sur la g麓eom麓etrie des espaces de Riemann, Gauthiers-Villars (1928).
    78.X. Chen, 鈥淩ecent progress in K盲hler geometry,鈥?in: Proc. Int. Congr. Mat. 2002, 2, 273鈥?82 (2002).
    79.J. T. Cho and K. Sekigawa, 鈥淪ix-dimensional quasi-K盲hlerian manifolds of constant sectional curvature,鈥?Tsukuba J. Math., 22, No. 3, 611鈥?27 (1998).MATH MathSciNet
    80.T. Choi and Z. Lu, 鈥淥n the DDVV conjecture and comass in calibrated geometry, I,鈥?Math. Z., 260, 409鈥?29 (2008).MATH MathSciNet
    81.V. Cortes, 鈥淪pecial Kaehler manifolds: a survey,鈥?Rend. Circ. Mat. Palermo, 69, 11鈥?8 (2002).
    82.R. Deszcz, F. Dillen, L. Verstraelen, and L. Vrancken, 鈥淨uasi-Einstein totally real submanifolds of nearly K盲hler 6-sphere,鈥?T么hoku Math. J., 51, 461鈥?78 (1999).MATH MathSciNet
    83.T. C. Draghici, 鈥淥n some 4-dimensional almost K盲hler manifolds,鈥?Kodai Math. J., 18, 156鈥?63 (1995).MATH MathSciNet
    84.T. C. Draghici, 鈥淎lmost K盲hler 4-manifolds with J-invariant Ricci tensor,鈥?Houston J. Math., 25, 133鈥?45 (1999).MATH MathSciNet
    85.S. Dragomir and L. Ornea, Locally Conformal K盲hler Geometry, Progr. Math., Birkh盲user, Boston (1998).
    86.B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Contemporary Geometry. Methods and Applications [in Russian], Nauka, Moscow (1986).
    87.B. Eckmann, 鈥淪tetige losungen linearer gleichungsysteme,鈥?Comment. Math. Helv., 15, 318鈥?39 (1942-1943).
    88.N. Ejiri, 鈥淭otally real submanifolds in a 6-sphere,鈥?Proc. Am. Math. Soc., 83, 759鈥?63 (1981).MATH MathSciNet
    89.H. Freudenthal, Oktaven, Ausnahmegruppen und Oktavengeometrie, Mathematisch Instituut der Rijksuniversiteit te Utrecht (1951).
    90.S. Funabashi and J. S. Pak, 鈥淭ubular hypersurfaces of the nearly K盲hler 6-sphere,鈥?Saitama Math. J., 19, 13鈥?6 (2001).MATH MathSciNet
    91.G. Ganchev and O. Kassabov, 鈥淗ermitian manifolds of pointwise constant antiholomorphic sectional curvatures,鈥?Serdica Math. J., 33, 377鈥?86 (2007).MATH MathSciNet
    92.G. Gheorghiev and V. Oproiu, Varietati diferentiabile finit si infinit dimensionale, Bucuresti Acad. RSR (1976鈥?979).
    93.S. Goldberg and S. Kobayashi, 鈥淗olomorphic bisectional curvature,鈥?J. Differ. Geom., 1, 225鈥?33 (1967).MATH MathSciNet
    94.A. Gray, 鈥淢inimal varieties and almost Hermitian submanifolds,鈥?Michigan Math. J., 12, 273鈥?87 (1965).MATH MathSciNet
    95.A. Gray, 鈥淪ome examples of almost Hermitian manifolds,鈥?Ill. J. Math., 10, No. 2, 353鈥?66 (1966).MATH
    96.A. Gray, 鈥淪ix-dimensional almost complex manifolds defined by means of three-fold vector cross products,鈥?T么hoku Math. J., 21, No. 4, 614鈥?20 (1969).MATH
    97.A. Gray, 鈥淰ector cross products on manifolds,鈥?Trans. Am. Math. Soc., 141, 465鈥?04 (1969).MATH
    98.A. Gray, 鈥淎lmost complex submanifolds of the six sphere,鈥?Proc. Am. Math. Soc., 20, 277鈥?80 (1969).MATH
    99.A. Gray, 鈥淣early K盲hler manifolds,鈥?J. Differ. Geom., 4, 283鈥?09 (1970).MATH
    100.A. Gray, 鈥淭he structure of nearly K盲hler manifolds,鈥?Math. Ann., 223, 223鈥?48 (1976).
    101.A. Gray, 鈥淐urvature identities for Hermitian and almost Hermitian manifolds,鈥?T么hoku Math. J., 28, No. 4, 601鈥?12 (1976).MATH
    102.A. Gray and L. M. Hervella, 鈥淭he sixteen classes of almost Hermitian manifolds and their linear invariants,鈥?Ann. Mat. Pura Appl., 123, No. 4, 35鈥?8 (1980).MATH MathSciNet
    103.H. Hashimoto, 鈥淐haracteristic classes of oriented 6-dimensional submanifolds in the octonions,鈥?Kodai Math. J., 16, 65鈥?3 (1993).MATH MathSciNet
    104.H. Hashimoto, 鈥淥riented 6-dimensional submanifolds in the octonions,鈥?Int. J. Math. Math. Sci., 18, 111鈥?20 (1995).MATH
    105.H. Hashimoto, T. Koda, K. Mashimo, and K. Sekigawa, 鈥淓xtrinsic homogeneous Hermitian 6-dimensional submanifolds in the octonions,鈥?Kodai Math. J., 30, 297鈥?21 (2007).MATH MathSciNet
    106.S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Pure Appl. Math., 80, Academic Press, New York鈥揝an Francisco鈥揕ondon (1978).
    107.L. Hernandez-Lamoneda, 鈥淐urvature vs almost Hermitian structures,鈥?Geom. Dedic., 79, 205鈥?18 (2000).MATH MathSciNet
    108.L. M. Hervella and E. Vidal, 鈥淣ovelles g猫om猫tries pseudo-kahl猫riennes G 1 et G 2,鈥?C. R. Acad. Sci. Paris. Ser. 1, 283, 115鈥?18 (1976).MathSciNet
    109.C. C. Hsiung, Almost Complex and Complex Structures, World Scientific, Singapore (1995).MATH
    110.N. E. Hurt, Geometric Quantization in Action. Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory, Math. Appl., 8, Reidel Publ., Dordrecht鈥揃oston鈥揕ondon (1983).
    111.S. Ianus, 鈥淪ubmanifolds of almost Hermitian manifolds,鈥?Riv. Mat. Univ. Parma, 3, 123鈥?42 (1994).MATH MathSciNet
    112.S. Ianus, Geometrie Diferentiala cu Aplicatii in Teoria Relativitatii, Editura Academiei Romane, Bucure,sti (1983).
    113.J. Jost, Riemannian Geometry and Geometric Analysis, Springer-Verlag, Berlin鈥揌eidelberg鈥揘ew York (2003).
    114.T. Kashiwada, 鈥淥n a class of locally conformal K盲hler manifolds,鈥?Tensor (N.S.), 63, 297鈥?06 (2002).MATH MathSciNet
    115.H. S. Kim and R. Takagi, 鈥淭he type number of real hypersurfaces in P n (C),鈥?Tsukuba J. Math., 20, 349鈥?56 (1996).MATH MathSciNet
    116.Un Kyu Kim, 鈥淥n six-dimensional almost Hermitian manifolds with pointwise constant holomorphic sectional curvature,鈥?Nihonkai Math. J., 6, 185鈥?00 (1995).
    117.V. F. Kirichenko, 鈥淎lmost K盲hlerian structures induced by 3-vector products on 6-dimensional submanifolds of Cayley algebras,鈥?Vestn. MGU. Ser. Mat. Mekh., 3, 70鈥?5 (1973).
    118.V. F. Kirichenko, 鈥?em class="EmphasisTypeItalic">K-spaces of the constant type,鈥?Sib. Mat. Zh., 17, No. 2, 282鈥?89 (1976).MATH
    119.V. F. Kirichenko, 鈥淐lassification of K盲hlerian structures induced by 3-vector products on 6-dimensional submanifolds of Cayley algebras,鈥?Izv. Vyssh. Uchebn. Zaved. Ser. Mat., 8, 32鈥?8 (1980).MathSciNet
    120.V. F. Kirichenko, 鈥淪tability of almost Hermitian structures induced by 3-vector products on 6-dimensional submanifolds of Cayley algebras,鈥?Ukr. Geom. Sb., 25, 60鈥?8 (1982).MATH MathSciNet
    121.V. F. Kirichenko, 鈥淭he tangent bundle from the point of view of generalized Hermitian geometry,鈥?Izv. Vyssh. Uchebn. Zaved. Ser. Mat., 6, 50鈥?8 (1984).
    122.V. F. Kirichenko, 鈥淢ethods of generalized Hermitian geometry in the theory of almost contact manifolds,鈥?in: Itogi Nauki Tekhn. Probl. Geom., 18, All-Russian Institute for Scientific and Technical Information (VINITI), Moscow (1986), pp. 25鈥?1.
    123.V. F. Kirichenko, 鈥淟ocally conformal K盲hlerian manifolds of a constant holomorphic sectional curvature,鈥?Mat. Sb., 182, No. 3, 354鈥?62 (1991).MATH
    124.V. F. Kirichenko, 鈥淗ermitian geometry of 6-dimensional symmetric submanifolds of Cayley algebras,鈥?Vestn. MGU. Ser. Mat. Mekh., 1, 6鈥?3 (1994).
    125.V. F. Kirichenko, Differential-Geometric Structures on Manifolds [in Russian], Moscow (2003).
    126.V. F. Kirichenko, 鈥淕eneralized Gray鈥揌ervella classes and holomorphically-projective trnsformations of almost Hermitian structures,鈥?Izv. Ross. Akad. Nauk. Ser. Mat., 69, No. 5, 107鈥?32 (2005).MathSciNet
    127.V. F. Kirichenko and N. A. Ezhova, 鈥淐onformal invariants of Vaisman鈥揋ray manifolds,鈥?Usp. Mat. Nauk, 51, No. 2, 163鈥?64 (1996).MathSciNet
    128.V. F. Kirichenko and N. N. Shchipkova, 鈥淥n the geometry of Vaisman鈥揋ray manifolds,鈥?Usp. Mat. Nauk, 49, No. 2, 155鈥?56 (1994).MathSciNet
    129.V. F. Kirichenko and L. I. Vlasova, 鈥淐oncircular geometry of approximately K盲hlerian manifolds,鈥?Mat. Sb., 193, No. 5, 51鈥?6 (2002).MathSciNet
    130.S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1, Interscience Publ. New York鈥揕ondon (1963).
    131.S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 2, Interscience Publ. New York鈥揕ondon (1969).
    132.M. Kon and K. Yano, Structures on Manifolds, Pure Math., 3, World Scientific (1984).
    133.H. Kurihara, 鈥淥n real hypersurfaces in a complex space form,鈥?Math. J. Okayama Univ., 40, 177鈥?86 (1998).MathSciNet
    134.H. Kurihara, 鈥淭he type number on real hypersurfaces in a quaternionic space form,鈥?Tsukuba J. Math., 24, 127鈥?32 (2000).MATH MathSciNet
    135.H. Kurihara and R. Takagi, 鈥淎 note on the type number of real hypersurfaces in P n (C),鈥?Tsukuba J. Math., 22, 793鈥?02 (1998).MathSciNet
    136.G. F. Laptev, 鈥淔undamental higher-orders infinitesimal structures on smooth manifolds,鈥?in: Tr. Geom. Semin., 1, All-Union Institute for Scientific and Technical Information (VINITI), Moscow (1966), pp. 139鈥?89.
    137.J. J. Levko, 鈥淪ome characterizations of K盲hlerian structure,鈥?Tensor (N.S.), 41, 249鈥?57 (1984).MATH MathSciNet
    138.J. J. Levko, 鈥淎lmost semi-K盲hlerian structure,鈥?Tensor (N.S.), 64, 295鈥?96 (2003).MATH MathSciNet
    139.H. Li, 鈥淭he Ricci curvature of totally real 3-dimensional submanifolds of the nearly Kaehler 6-sphere,鈥?Bull. Belg. Math. Soc. Simon Stevin., 3, 193鈥?99 (1996).MATH MathSciNet
    140.H. Li and G. Wei, 鈥淐lassification of Lagrangian Willmore submanifolds of the nearly Kaehler 6-sphere S 1 6 with constant scalar curvature,鈥?Glasgow Math. J., 48, 53鈥?4 (2006).MathSciNet
    141.A. Lichnerowicz, Th麓orie globale des connexions et des groupes d鈥檋olonomie, Rome, Edizioni Cremonese (1955).
    142.D. Luczyszyn, 鈥淥n para-K盲hlerian manifolds with recurrent paraholomorphic projective curvature,鈥?Math. Balkanica (N.S.), 14, 167鈥?76 (2000).MATH MathSciNet
    143.D. Luczyszyn, 鈥淥n Bochner semisymmetric para-K盲hlerian manifolds,鈥?Demonstr. Math., 4, 933鈥?42 (2001).MathSciNet
    144.D. Luczyszyn, 鈥淥n pseudosymmetric para-K盲hlerian manifolds,鈥?Beitr盲ge Algebra Geom., 44, No. 2, 551鈥?58 (2003).MATH MathSciNet
    145.G. Mari, 鈥淐urvature identities for an almost C-manifold,鈥?Stud. Cerc. Mat., 50, Nos. 1-2, 23鈥?8 (1998).MATH MathSciNet
    146.M. Matsumoto, 鈥淥n 6-dimensional almost Tachibana spaces,鈥?Tensor (N.S.), 23, 250鈥?52 (1972).MATH MathSciNet
    147.P. Matzeu and M.-I. Munteanu, 鈥淰ector cross products and almost contact structures,鈥?Rend. Mat. Roma, 22, 359鈥?76 (2002).MATH MathSciNet
    148.A. S. Mishchenko and A. T. Fomenko, A Course in Differential Geometry and Topology [in Russian], Moscow (1980).
    149.R. S. Mishra, 鈥淣ormality of the hypersurfaces of almost Hermite manifolds,鈥?J. Indian Math. Soc., 61, 71鈥?9 (1995).MATH MathSciNet
    150.M. I. Munteanu, 鈥淒oubly warped products CR-submanifolds in locally conformal Kaehler manifolds,鈥?Monatsh. Math., 150, No. 4, 333鈥?42 (2007).MATH MathSciNet
    151.P.-A. Nagy, 鈥淥n nearly-K盲hler geometry,鈥?Ann. Global Anal. Geom., 22, 167鈥?78 (2002).MATH MathSciNet
    152.H. Nakagawa and R. Takagi, 鈥淥n locally symmetric Kaehler submanifolds in a complex projective space,鈥?J. Math. Soc. Jpn., 28, 638鈥?67 (1976).MATH MathSciNet
    153.A. Nannicini, 鈥淥n certain K盲hler submanifolds of twistor spaces,鈥?Boll. Unione Mat. Ital. Sez. B, 11, 257鈥?65 (1997).MATH MathSciNet
    154.A. P. Norden, Theory of Surfaces [in Russian], Moscow (1956).
    155.V. Oproiu, 鈥淪ome classes of natural almost Hermitian structures on the tangent bundles,鈥?Publ. Math. Debrecen., 62, Nos. 3鈥?, 561鈥?76 (2003).MATH MathSciNet
    156.V. Oproiu, 鈥淪ome classes of general natural almost Hermitian structures on tangent bundles,鈥?Rev. Roum. Math. Pures Appl., 48, Nos. 5鈥?, 521鈥?33 (2003).MATH MathSciNet
    157.M. Panak and J. Vanzura, 鈥淭hree-forms and almost complex structures on six-dimensional manifolds,鈥?J. Austr. Math. Soc., 84, 247鈥?63 (2008).MATH MathSciNet
    158.V. I. Pan鈥檢henskii and K. B. Shiryaev, 鈥淭ensor signs of classes of almost Hermitian structures on the tangent bundle,鈥?in: Motions in Generalized Spaces [in Russian], Penza (1999), pp. 126鈥?32.
    159.A. Z. Petrov, Einstein Spaces [in Russian], Moscow (1961).
    160.M. M. Postnikov, Lectures in Geometry. Semester IV. Differential Geometry [in Russian], Nauka, Moscow (1988).
    161.P. K. Rashevskii, Riemannian Geometry and Tensor Analysis [in Russian], Nauka, Moscow (1967).
    162.G. B. Rizza, 鈥淰arieta parak盲hleriane,鈥?Ann. Mat. Pura Appl., 98, 47鈥?1 (1974).MATH MathSciNet
    163.P. J. Ryan, 鈥淜盲hler manifolds as real hypersurfaces,鈥?Duke Math. J., 40, 207鈥?13 (1973).MATH MathSciNet
    164.T. Sato, 鈥淎n example of an almost K盲hler manifold with pointwise constant holomorphic sectional curvature,鈥?Tokyo J. Math., 23, No. 2, 387鈥?01 (2000).MATH MathSciNet
    165.S. Sawaki and K. Sekigawa, 鈥淎lmost Hermitian manifolds with constant holomorphic sectional curvature,鈥?J. Differ. Geom., 9, 123鈥?34 (1974).MATH MathSciNet
    166.K. Sekigawa, 鈥淎lmost Hermitian manifolds satisfying some curvature conditions,鈥?Kodai Math. J., 2, 384鈥?05 (1979).MATH MathSciNet
    167.K. Sekigawa, 鈥淎lmost complex submanifolds of a six-dimensional sphere,鈥?Kodai Math. J., 6, 174鈥?85 (1983).MATH MathSciNet
    168.K. Sekigawa, 鈥淥n some compact Einstein almost K盲hler manifolds,鈥?J. Math. Soc. Jpn., 36, 677鈥?84 (1987).MathSciNet
    169.K. Sekigawa, 鈥淥n some 4-dimensional compact almost Hermitian manifolds,鈥?J. Ramanujan Math. Soc., 2, 101鈥?16 (1987).MATH MathSciNet
    170.S. S. Shern, M. P. Do Carmo, and S. Kobayashi, 鈥淢inimal submanifolds of a sphere with second fundamental form of constant length,鈥?in: Functional Analysis and Related Fields, Springer- Verlag, Berlin (1970), pp. 59鈥?5.
    171.R. Takagi, 鈥淎 class of hypersurfaces with constant principal curvatures in a sphere,鈥?J. Differ. Geom., 11, 225鈥?33 (1976).MATH
    172.Z. Tang, 鈥淐urvature and integrability of an almost Hermitian structure,鈥?Int. J. Math., 27, No. 1, 97鈥?05 (2006).
    173.S. Tanno, 鈥淐onstancy of holomorphic sectional curvature in almost Hermitian manifolds,鈥?Kodai Math. Semin. Repts., 25, 190鈥?01 (1973).MATH MathSciNet
    174.S. Tanno, 鈥淩icci curvature of contact Riemannian manifolds,鈥?T么hoku Math. J., 40, 441鈥?48 (1988).MATH MathSciNet
    175.M. Tekkoyun, 鈥淎 general view to classification of almost Hermitian manifolds,鈥?Rend. Inst. Mat. Univ. Trieste, 38, 1鈥?5 (2006).MATH MathSciNet
    176.F. Tricerri, 鈥淪ome examples of locally conformal K盲hler manifolds,鈥?Rend. Sem. Mat. Univ. Politec. Torino, 40, 81鈥?2 (1982).MATH MathSciNet
    177.F. Tricerri and L. Vanhecke, 鈥淐urvature tensors on almost Hermitian manifolds,鈥?Trans. Am. Math. Soc., 267, 365鈥?98 (1981).MATH MathSciNet
    178.I. Vaisman, 鈥淥n locally conformal almost K盲hler manifolds,鈥?Israel J. Math., 24, 338鈥?51 (1976).MATH MathSciNet
    179.I. Vaisman, 鈥淥n locally and globally conformal K盲hler manifolds,鈥?Trans. Am. Math. Soc., 2, 533鈥?42 (1980).MathSciNet
    180.L. Vanhecke, 鈥淎lmost Hermitian manifolds with J-invariant Riemann curvature tensor,鈥?Rend. Sem. Mat. Univ. Politec. Torino, 34, 487鈥?98 (1975鈥?977).
    181.L. Vanhecke, 鈥淭he Bochner curvature tensor on almost Hermitian manifolds,鈥?Geom. Dedic., 6, 389鈥?97 (1977).MATH MathSciNet
    182.L. Vrancken, 鈥淪pecial Lagrangian submanifolds of the nearly Kaehler 6-sphere,鈥?Glasgow Math. J., 45, 415鈥?26 (2003).MATH MathSciNet
    183.B. Watson, 鈥淣ew examples of strictly almost K盲hler manifolds,鈥?Proc. Am. Math. Soc., 88, 541鈥?44 (1983).MATH
    184.G. Whitehead, 鈥淣ote on cross-sections in Stiefel manifolds,鈥?Comment. Math. Helv., 34, 239鈥?40 (1962).MathSciNet
    185.K. Yano, Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, Oxford (1965).MATH
    186.K. Yano and S. Ishihara, 鈥淎lmost contact structures induced on hypersurfaces in complex and almost complex spaces,鈥?Kodai Math. Sem. Rep., 17, No. 3, 222鈥?49 (1965).MATH MathSciNet
    187.K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore (1984).MATH
    188.K. Yano and T. Sumitomo, 鈥淒ifferential geometry of hypersurfaces in a Cayley space,鈥?Proc. Roy. Soc. Edinburgh. Sec. A, 66, 216鈥?31 (1962鈥?964).
  • 作者单位:M. B. Banaru (1)

    1. Smolensk State University, Smolensk, Russia
  • 刊物类别:Mathematics and Statistics
  • 刊物主题:Mathematics
    Mathematics
    Russian Library of Science
  • 出版者:Springer New York
  • ISSN:1573-8795
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