Hemi-slant Submanifolds Research Articles

Warped Product Submanifolds of LP‐Sasakian Manifolds

We study of warped product submanifolds, especially warped product hemi‐slant submanifolds of LP‐Sasakian manifolds. We obtain the results on the nonexistance or existence of warped product hemi‐slant submanifolds and give some examples of LP‐Sasakian manifolds. The existence of warped product hemi‐slant submanifolds of an LP‐Sasakian manifold is also ensured by an interesting example.

Totally Umbilical Proper Slant and Hemislant Submanifolds of an LP‐Cosymplectic Manifold

In the present note, we study slant and hemislant submanifolds of an LP‐cosymplectic manifold which are totally umbilical. We prove that every totally umbilical proper slant submanifold M of an LP‐cosymplectic manifold is either totally geodesic or if M is not totally geodesic in then we derive a formula for slant angle of M. Also, we obtain the integrability conditions of the distributions of a hemi‐slant submanifold, and then we give a result on its classification.

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

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.