In this paper, we introduce some inequalities for screen homothetic half lightlike submanifolds of a real space form constant sectional curvature , endowed with semi-symmetric metric connection. Using these inequalities, derive characterizations such submanifolds. Finally, Chen-Ricci are calculated. Morever, the equality cases considered and get results.

The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found necessary condition under which vector field manifold will be strict contact field. Then, we obtained extended generalized phi-recurrent with respect connection. Next, satises ~L.~ S = 0 studied.

Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most homogeneous case. In this direction, famous ones are results by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov other At same time, studying little for case an arbitrary metri...

We consider a nearly hyperbolic Sasakian manifold endowed with a quarter symmetric non-metric connection and study CRsubmanifolds of nearly hyperbolic Sasakian manifold endowed with a quarter symmetric nonmetric connection. We also obtain parallel distributions and discuss inerrability conditions of distributions on CR-submanifolds of nearly hyperbolic Sasakian manifold with quarter symmetric n...

We obtain curvature tensor R̃(X, Y )Z w.r.t quarter-symmetric metric connection in terms of curvature tensor R(X,Y )Z relative to the Levi-civita connection in a K-contact manifold. Further, locally φ-symmetric, φ-symmetric and locally projective φ-symmetric K-contact manifolds with respect to the quarter-symmetric metric connection are studied and some results are obtained. The results are assi...

In the present paper, we discuss singular minimal surfaces in Euclidean $3-$space $\mathbb{R}^{3}$ which are minimal. Such a surface is nothing but plane, trivial outcome. However, non-trivial outcome obtained when modify usual condition of minimality by using special semi-symmetric metric connection instead Levi-Civita on $\mathbb{R}^{3}$. With this new connection, prove that, besides planes, ...

In this paper, we prove the DDVV conjecture for a slant submanifold in metallic Riemannian space forms with semi-symmetric metric connection. The equality case of derived inequality is discussed, and some special cases are given.