Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex projective space

Abstract

We study m-dimensional real submanifolds M with (m − 1)-dimensional maximal holomorphic tangent subspace in complex projective space. On these manifolds there exists an almost contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX, Y) − h(X, FY) = g(FX, Y)η, η ∈ T⊥(M), on the almost contact structure F and on the second fundamental form h of these submanifolds and we characterize certain model spaces in complex projective space.