Abstract. In this paper we prove that a ϕ-recurrent (k, µ)-contact metric manifold is an η-Einstein manifold with constant coefficients. Next, we prove that a three-dimensional locally ϕ-recurrent (k, µ)-contact metric manifold is the space of constant curvature. The existence of ϕ-recurrent (k, µ)-manifold is proved by a non-trivial example.
We consider pseudo-symmetric and Ricci generalized pseudo-symmetric N (κ)contact metric manifolds. We also consider N (κ)-contact metric manifolds satisfying the condition S · R = 0 where R and S denote the curvature tensor and the Ricci tensor respectively. Finally we give some examples.
Abstract. We define a semi-symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.
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