Some submanifolds of generalized Kenmotsu manifolds

Abstract

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied and given some properties. An example is constructed for an invariant submanifold of a generalized Kenmotsu manifold. In addition, integrabilities of invariant distribution is investigated, and some theorems are given related to curvature tensor and the second fundamental form in invariant submanifolds of a generalized Kenmotsu manifold. Moreover, semi-parallel and 2-semi-parallel invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on semi-parallel and 2-semi-parallel invariant submanifolds of a generalized Kenmotsu manifold to be totally geodesic.