Department of Mathematics, Kuvempu University, Shankaraghatta, Karnataka, Shimoga 577451, India
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 of Sasakian manifolds admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms
and with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form 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.