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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 947640, 18 pages
Research Article

Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection

Department of Mathematics, Kuvempu University, Shankaraghatta, Karnataka, Shimoga 577451, India

Received 30 March 2012; Accepted 2 July 2012

Academic Editor: V. R. Khalilov

Copyright © 2012 B. S. Anitha and C. S. Bagewadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The object of this paper is to study invariant submanifolds 𝑀 of Sasakian manifolds 𝑀 admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms 𝜎 and 𝜎 with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form 𝜎 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.