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Submersions of generic submanifolds of a Kaehler manifold

By Tanveer Fatima and Shahid Ali

Abstract

Kobayashi has shown that for the submersion π:M→B of a CR-submanifold of a Kaehler manifold M¯ onto an almost Hermitian manifold B,B is necessarily a Kaehler manifold. Since generic submanifolds are more general class of CR-submanifolds, in this present article we study the submersions of generic submanifolds M of a Kaehler manifold M¯ onto an almost Hermitian manifold B and prove that B is necessarily a Kaehler manifold in this case too. We also obtain the decomposition theorems for such submersions and derive the relation between the holomorphic sectional curvatures of M¯ restricted to D and that of B. Also the geometry of fibres is discussed

Topics: Riemannian submersions, Almost Hermitian submersions, Generic submanifolds, Decomposition theorems, Mathematics, QA1-939
Publisher: Elsevier
Year: 2014
DOI identifier: 10.1016/j.ajmsc.2013.05.003
OAI identifier: oai:doaj.org/article:fb17139f3d154d0ca000fb4acb45ee05
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