Invariant Submanifolds of Trans-Sasakian Manifolds

Abstract

We prove the equivalence of total geodesicity, recurrence, birecurrence, generalized birecurrence, Riccigeneralized birecurrence, parallelism, biparallelism, pseudoparallelism, bipseudoparallelism of σσ for the invariant submanifold $M$ of the trans-Sasakian manifold $\tilde{M}$.