A classification of totally umbilical proper slant and hemi-slant submanifolds of (k, μ)-contact manifolds

Abstract

The object of the present paper is to study slant and hemi-slant submanifolds of (k, μ)- contact manifolds which are totally umbilical. We prove that every totally umbilical proper slant submanifold M of a (k, μ)-contact manifold ˜M is either totally geodesic or if M is not totally geodesic then we derive a formula for slant angle. Also necessary and sufficient conditions for distributions of hemi-slant submanifolds to be integrable are worked out. Further we give a characterization theorem.