Abstract
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.
Highlights
For an invariant submanifold of a Sasakian manifold with a Semisymmetric Nonmetric connection we have σ X, ξ 0, 4.1 for any vector X tangent to M
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
Summary
For an invariant submanifold of a Sasakian manifold with a Semisymmetric Nonmetric connection we have σ X, ξ 0, 4.1 for any vector X tangent to M. An immersion is said to be semiparallel, pseudoparallel, and Ricci-generalized pseudoparallel with respect to Semisymmetric Nonmetric connection, respectively, if the following conditions hold for all vector fields X, Y tangent to M: R · σ 0, R · σ L1Q g, σ , 4.6
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