Khushwant Singh

Warped Product Semi-Invariant Submanifolds of Nearly Cosymplectic Manifolds

We study warped product semi-invariant submanifolds of nearly cosymplectic manifolds. We prove that the warped product of the type 𝑀⟂×𝑓𝑀𝑇 is a usual Riemannian product of 𝑀⟂ and 𝑀𝑇, where 𝑀⟂ and 𝑀𝑇 are anti-invariant and invariant submanifolds of a nearly cosymplectic manifold 𝑀, respectively. Thus we consider the warped product of the type 𝑀𝑇×𝑓𝑀⟂ and obtain a characterization for such type of warped product.

A class of totally umbilical slant submanifolds of Lorentzian para-Sasakian manifolds

In the present paper, we study slant submanifolds of a Lorentzian para (LP)-Sasakian manifold. We consider as a totally umbilical proper slant submanifold of an LP-Sasakian manifold and show that every totally umbilical proper slant submanifold of an LP-Sasakian manifold is either totally geodesic or if it is not totally geodesic in , then we derive a formula of its slant angle and give an 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 𝑀 is either totally geodesic or if 𝑀 is not totally geodesic in 𝑀 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.