On contact submanifolds in complex projective spaces

Abstract

We treat n-dimensional real submanifolds of complex projective spaces in the case when the maximal holomorphic tangent subspace is (n - 1)-dimensional. In particular, we study the case when the induced almost contact structure on a submanifold is contact, we establish a few characteristics of the shape operator with respect to the distinguished vector field and we give one characterization of a contact submanifold in this case.