Invariant Submanifolds of Sasakian Manifolds Admitting Semi-symmetric Metric Connection - Anitha, B. S.; Bagewadi, C. S. (Communications in Mathematics and Applications, 2013)
The object of this paper is to study invariant submanifolds M of Sasakian manifolds 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 σ and σ with respect to Levi-Civita connection and semi-symmetric metric connection coincide. It is shown that if the second fundamental form σ 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.