Invariant Submanifolds of Sasakian Manifolds Admitting Semi-symmetric Metric Connection

B. S. Anitha, C. S. Bagewadi

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.

Keywords


Invariant submanifolds; Sasakian manifold; Semi-symmetric metric connection; Totally geodesic

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DOI: http://dx.doi.org/10.26713%2Fcma.v4i1.160

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