ON Φ-RECURRENT (k, μ)-CONTACT METRIC MANIFOLDS

Abstract

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.

On a Subclass of (k, µ)-Contact Metric Manifolds

“…If ξ ∈ N (k), we call contact metric manifold M an N(k)-contact metric manifold. (k, µ)-contact metric manifolds have been studied by several authors ( [5], [6], [7]) and many authors.…”

Certain Semisymmetry Properties of (𝜅, 𝜇)-Contact Metric Manifolds

“…(κ, µ)-contact metric manifolds have been studied by several authors ( [1], [4], [5], [6], [7], [9]) and many other authors.…”

E-Bochner CURVATURE TENSOR ON ( Κ , Μ)-Contact METRIC MANIFOLDS

“…If ξ ∈ N (κ) , then we call contact metric manifold M an N(κ)-contact metric manifold. (κ, µ)-contact metric manifolds have been studied by several authors ( [16], [1], [8], [10], [11], [12]) and many others.…”