Invariant Submanifolds of Sasakian Manifolds Admitting Semi-symmetric Metric Connection

Abstract

The object of this paper is to study invariant submanifolds $M$ of Sasakian manifolds $\widetilde{M}$ admitting a semi-symmetric metric connection and to show that $M$ admits semi-symmetric metric connection. Further it is proved that the second fundamental forms $\sigma$ and $\overline{\sigma}$ with respect to Levi-Civita connection and semi-symmetric metric connection coincide. It is shown that if the second fundamental form $\sigma$ is recurrent, 2-recurrent, generalized 2-recurrent and $M$ has parallel third fundamental form with respect to semi-symmetric metric connection, then $M$ is totally geodesic with respect to Levi-Civita connection.