A CLASSIFICATION OF (Κ, Μ)-Contact METRIC MANIFOLDS

Abstract

In this paper we study h-projectively semisymmetric, ϕ-projectively semisymmetric, h-Weyl semisymmetric and ϕ-Weyl semisymmetric non-Sasakian (k, µ)-contact metric manifolds. In all the cases the manifold becomes an η-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian (k, µ)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N (k)-contact metric manifold.

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

“…However, Yildiz and De [13] proved the following: Proposition 3.1. In a non-Sasakian (κ, µ)-contact metric manifold, the following conditions are equivalent:…”

“…Recently, in [13] Yildiz and De studied ϕ-projectively semisymmetric and h-projectively semisymmetric (κ, µ)-contact metric manifolds.…”

Eta-Ricci solitons on LP-Sasakian manifolds

“…In [29] Yildiz et al studied ϕ-conformally semi-symmetric (k, µ)-contact manifolds. A contact metric manifold is said to be ϕ-conformally semi-symmetric if C • ϕ = 0, where C is the conformal curvature tensor.…”

Η-Ricci SOLITONS ON 3-Dimensional N(k)-Contact METRIC MANIFOLDS

“…In a recent paper Yildiz et al [26] studied φ-Weyl semisymmetric and h-Weyl semisymmetric (k, µ)-contact manifolds. A (k, µ)-contact manifold is said to be φ-Weyl semisymmetric if C.φ = 0 and h-Weyl semisymmetric if C.h = 0, where C is the Weyl conformal curvature tensor.…”