Abdul Haseeb

Hypersurfaces of an almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Non-metric Connection

We define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection.

HYPERSURFACES OF ALMOST γ-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A QUARTER SYMMETRIC METRIC CONNECTION

We define a quarter symmetric metric connection in an al- most r-paracontact Riemannian manifold and we consider invariant, non- invariant and anti-invariant hypersurfaces of an almost r-paracontact Rie- mannian manifold endowed with a quarter symmetric metric connection.

On semi-invariant submanifolds of a nearly Sasakian manifold admitting a semi-symmetric non-metric connection

Abstract We define a semi-symmetric non-metric connection in a nearly Sasakian manifold and we consider semi-invariant submanifolds of a nearly Sasakian manifold endowed with a semi-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

ON ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD WITH A CERTAIN CONNECTION

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several sym- metric, semi-symmetric and quarter symmetric connections, even some of them are not introduced so far. So, in this paper, we deflne a quarter symmetric semi-metric connection in an almost r-paracontact Riemann- ian manifold and consider invariant, non-invariant and anti-invariant hy- persurfaces of an almost r-paracontact Riemannian manifold with that connection.