Submersions of generic submanifolds of a Kaehler manifold

Kobayashi has shown that for the submersion π:M→Bπ: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 DD and that of B. Also the geometry of fibres is discussed.