Submanifolds of F-structure manifold satisfying FK+(−)K+1F=0

Abstract

The purpose of this paper is to study invariant submanifolds of an n-dimensional manifold M endowed with an F-structure satisfying FK+(−)K+1F=0 and FW+(−)W+1F≠0 for 1<W<K, where K is a fixed positive integer greater than 2. The case when K is odd (≥3) has been considered in this paper. We show that an invariant submanifold M˜, embedded in an F-structure manifold M in such a way that the complementary distribution Dm is never tangential to the invariant submanifold ψ(M˜), is an almost complex manifold with the induced F˜-structure. Some theorems regarding the integrability conditions of induced F˜-structure are proved.