Commutative condition on the second fundamental form of CR-submanifolds of maximal CR-dimension of a Kähler manifold

Abstract

We study m-dimensional real submanifolds of codimension p with (m − 1)-dimensional maximal holomorphic tangent subspace in a Kähler manifold. Consequently, on these manifolds there exists an almost contact structure (F, u,U, g) naturally induced from the ambient space. In this paper, we study a certain commutative condition on the almost contact structure and on the second fundamental form of these submanifolds.