Submersions of generic submanifolds of a Kaehler manifold

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.

Keywords

• Riemannian submersions
• Almost Hermitian submersions
• Generic submanifolds
• Decomposition theorems