Submersions of generic submanifolds of a Kaehler manifold

Submersions of generic submanifolds of a Kaehler manifold

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 su...

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Bibliographic Details
Main Authors: Tanveer Fatima, Shahid Ali
Format: Article
Language:English
Published: Emerald Publishing 2014-01-01
Series:Arab Journal of Mathematical Sciences
Subjects:
Riemannian submersions
Almost Hermitian submersions
Generic submanifolds
Decomposition theorems
Online Access:http://www.sciencedirect.com/science/article/pii/S1319516613000145
Description
Summary: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.
ISSN:1319-5166

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