Invariant Submanifolds of Sasakian Manifolds Admitting Semi-symmetric Metric Connection

Authors

  • B. S. Anitha Department of Mathematics, Kuvempu University, Shankaraghatta 577451, Shimoga, Karnataka
  • C. S. Bagewadi Department of Mathematics, Kuvempu University, Shankaraghatta 577451, Shimoga, Karnataka

DOI:

https://doi.org/10.26713/cma.v4i1.160

Keywords:

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

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.

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CITATION

How to Cite

Anitha, B. S., & Bagewadi, C. S. (2013). Invariant Submanifolds of Sasakian Manifolds Admitting Semi-symmetric Metric Connection. Communications in Mathematics and Applications, 4(1), 29–38. https://doi.org/10.26713/cma.v4i1.160

Issue

Section

Research Article