Product theorems on anti-invariant Riemannian submersions

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• 作者：Shahid Ali ; T. Fatima
• 关键词：Anti ; invariant Riemannian submersion ; Langrangian Riemannian submersion ; Totally geodesicness ; 53C15 ; 53C40 ; 53C50
• 刊名：Afrika Matematika
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：26
• 期：3-4
• 页码：471-483
• 全文大小：420 KB
• 参考文献：1.Ali, S., Fatima, T.: Integrability conditions for the distribution of anti-invariant Riemannian Submersions. J. Tensor Soc. 6(2), 163-75 (2012)MATH MathSciNet
  2.Baird, P., Wood, J.C.: Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs. Oxford University Press, Clarendon Press, Oxford (2003)View Article
  3.Bejancu, A.: Geometry of CR-Submanifolds. D. Reidel, Dordrecht (1986)View Article MATH
  4.Chinea, D.: Almost contact metric submersions. Rend. Circ. Mat. Palermo 34(1), 89-04 (1985)View Article MATH MathSciNet
  5.Escobales Jr, R.H.: Riemannian submersions from complex projective spaces. J. Differential Geom. 13(1), 93-07 (1978)MATH MathSciNet
  6.Gray, A.: Nearly Kaehler manifolds. J. Diff. Geom. 4, 238-09 (1970)
  7.Gray, A.: Some examples of almost Hermitian manifolds. Illinois J. Math 10, 353-66 (1966)MATH MathSciNet
  8.Marrero, J.C., Rocha, J.: Locally conformal Kaehler submersions. Geom. Dedicata 52(3), 271-89 (1994)View Article MATH MathSciNet
  9.O’Neill, B.: The fundamental equations of a submersion. Mich. Math. J. 13, 458-69 (1966)MathSciNet
  10.O’Neill, B.: Submersions and geodesics. Duke Math. J. 34, 459-69 (1966)
  11.Ponge, R., Reckziegel, H.: Twisted product in Pseudo-Riemannian geometry. Geom. Dedicata 48(1), 15-5 (1993)View Article MATH MathSciNet
  12.Sahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Cent. Eur. J. Math. 8(3), 437-47 (2010)View Article MATH MathSciNet
  13.Watson, B.: Almost Hermitian submersions. J. Differ. Geom. 11(1), 147-65 (1976)MATH
  14.Yano, K., Kon, M.: Structures on Manifolds. World Scientific, Singapore (1984)MATH
  
• 作者单位：Shahid Ali (1)
  T. Fatima (1) (2)
  
  1. Department of Mathematics, Aligarh Muslim University, Aligarh?, 202002, India
  2. Science College for Girls, Jazan University, Jazan?, 6841, Kingdom of Saudi Arabia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

In Ali and Fatima (J Tensor Soc 6(2):163-75, 2012) we studied anti-invariant and Langrangian Riemannian submersions from nearly kaehler manifolds. In this paper we have continued the study of such submersion and investigate the geometry of the leaves of two distributions and obtain the necessary and sufficient conditions for a Langrangian Riemannian submersions to be totally geodesic map. In the end, the decomposition theorems for the total manifold of the submersion are obtained.