Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection

Abstract EN

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.