Submersions of generic submanifolds of a Kaehler manifold | Zendy

Tanveer Fatima | Zendy; S. Ali | Zendy

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Submersions of generic submanifolds of a Kaehler manifold

Author(s) -

Tanveer Fatima,

S. Ali

Publication year - 2013

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2013.05.003

Subject(s) - mathematics , kähler manifold , pure mathematics , submanifold , holomorphic function , hermitian manifold , manifold (fluid mechanics) , hermitian matrix , complex manifold , mathematical analysis , ricci curvature , curvature , geometry , mechanical engineering , engineering

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

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