复Kropina度量
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摘要
讨论了复Kropina度量成为复Berwald度量的3个不同条件.研究了复Kropina度量的全纯曲率.特别是在β全纯的情况下,得到了复Kropina度量和Hermitian度量之间的全纯曲率关系.找到了复Kropina度量成为复Berwald度量的第4个条件,讨论了迷向全纯曲率.
In this paper we firstly discuss three different conditions that the complex Kropina metric becomes the complex Berwald metric.Next we study the holomorphic curvature of the complex Kropina metrics.Especially with holomorphicβwe obtain the holomorphic curvature relations between the complex Kropina metric and the purely Hermitian metric.Additionaly,the fourth condition being the complex Berwald metric is also found.Then we discuss isotropic holomorphic curvature.
In this paper we firstly discuss three different conditions that the complex Kropina metric becomes the complex Berwald metric.Next we study the holomorphic curvature of the complex Kropina metrics.Especially with holomorphicβwe obtain the holomorphic curvature relations between the complex Kropina metric and the purely Hermitian metric.Additionaly,the fourth condition being the complex Berwald metric is also found.Then we discuss isotropic holomorphic curvature.
引文
[1]Kropina V K.On projective Finsler spaces with a metric of some special form(in Russian)[J].Naun Dokl Vys.koly Fis Mat,1959,2:38-42.
[2]Antonelli P L,Ingarden R S,Matsumoto M.The theory of sprays and Finsler spaces with applications in physics and biology[M].Netherlands:Kluwer Academic Publishers,1993.
[3]Shibara C.On Finsler spaces with Kropina metric[J].Rep on Math Phys,1978,13:117-128.
[4]Matsumoto M.Finsler space of constant curvature with Kropina metric[J].Tensor N S,1991,50:194-201.
[5]Yoshikawa R,Okubo R.Kropina spaces of constant curvature[J].Tensor N S,2007,68:190-203.
[6]Singh U P,Singh A K,Shibata C.On induced and intrinsic theories of hypersurfaces of Kropina spaces[J].J Hokkaido Univ Education(SectionⅡA),1983,34:1-11.
[7]Munteanu G.Complex spaces in Finsler,lagrange and Hamilton geometries[M].Netherlands:Kluwer Acad Publ,2004.
[8]Aldea N,Munteanu G.On complex Finsler spaces with Randers metric[J].J Korean Math Soc,2009,46(5):949-966.
[9]Chen B,Shen Y B.On complex Randers metrics[J].Int J Math,2010,21(8):971.
[10]Aikou T.Some remarks on locally conformal complex Berwald spaces[J].Contemporary Mathematics,1996,196:109-120.
[11]Aldea N,Munteanu G.(α,β)-complex Finsler metrics[C]∥Proceedings of the 4th International Colloquium"Mathematics in Engineering and Numerical Physics".Bucharest:Balkan Press,2007:1-6.
[12]Abate M,Patrizio G.Finsler metrics:aglobal approach[M].Berlin:Springer-Verlag,1994.
[13]Chen B,Shen Y B.Kaehler Finsler metrics are actually strongly Kaehler[J].Chinese Annals of Mathematics:Series B,2009,30(2):173-178.
[14]Aldea N.Complex Finsler spaces of constant holomorphic curvature[C]∥Diff Geom and its Appl.Prague,Czech Republic:Charles Univ,2005:175-186.
[2]Antonelli P L,Ingarden R S,Matsumoto M.The theory of sprays and Finsler spaces with applications in physics and biology[M].Netherlands:Kluwer Academic Publishers,1993.
[3]Shibara C.On Finsler spaces with Kropina metric[J].Rep on Math Phys,1978,13:117-128.
[4]Matsumoto M.Finsler space of constant curvature with Kropina metric[J].Tensor N S,1991,50:194-201.
[5]Yoshikawa R,Okubo R.Kropina spaces of constant curvature[J].Tensor N S,2007,68:190-203.
[6]Singh U P,Singh A K,Shibata C.On induced and intrinsic theories of hypersurfaces of Kropina spaces[J].J Hokkaido Univ Education(SectionⅡA),1983,34:1-11.
[7]Munteanu G.Complex spaces in Finsler,lagrange and Hamilton geometries[M].Netherlands:Kluwer Acad Publ,2004.
[8]Aldea N,Munteanu G.On complex Finsler spaces with Randers metric[J].J Korean Math Soc,2009,46(5):949-966.
[9]Chen B,Shen Y B.On complex Randers metrics[J].Int J Math,2010,21(8):971.
[10]Aikou T.Some remarks on locally conformal complex Berwald spaces[J].Contemporary Mathematics,1996,196:109-120.
[11]Aldea N,Munteanu G.(α,β)-complex Finsler metrics[C]∥Proceedings of the 4th International Colloquium"Mathematics in Engineering and Numerical Physics".Bucharest:Balkan Press,2007:1-6.
[12]Abate M,Patrizio G.Finsler metrics:aglobal approach[M].Berlin:Springer-Verlag,1994.
[13]Chen B,Shen Y B.Kaehler Finsler metrics are actually strongly Kaehler[J].Chinese Annals of Mathematics:Series B,2009,30(2):173-178.
[14]Aldea N.Complex Finsler spaces of constant holomorphic curvature[C]∥Diff Geom and its Appl.Prague,Czech Republic:Charles Univ,2005:175-186.