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Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection

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  • B. S. Anitha
  • C. S. Bagewadi

Abstract

The object of this paper is to study invariant submanifolds 𠑀 of Sasakian manifolds  𠑀 admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms 𠜎 and 𠜎 with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form 𠜎 is recurrent, 2-recurrent, generalized 2-recurrent, semiparallel, pseudoparallel, and Ricci-generalized pseudoparallel and M has parallel third fundamental form with respect to semisymmetric nonmetric connection, then M is totally geodesic with respect to Levi-Civita connection.

Suggested Citation

  • B. S. Anitha & C. S. Bagewadi, 2012. "Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, August.
    • Handle: RePEc:hin:jijmms:947640
    DOI: 10.1155/2012/947640
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