Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection

B. S. Anitha and C. S. Bagewadi

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-18

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:947640

DOI: 10.1155/2012/947640

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