Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces

Abstract

The aim of this paper is to classify $(k,\mu)$-paracontact metric spaces satisfying certain curvature conditions. We present the curvature tensors of (k,$\mu $)-Paracontact manifold satisfying the conditions $R\cdot W_{6}=0$, $ R\cdot W_{7}=0$, $R\cdot W_{8}=0$ and $R\cdot W_{9}=0$. According these cases, $(k,\mu)$-Paracontact manifolds have been characterized. Also, several results are obtained.

Keywords

• (k.mu)-paracontact manifold
• eta-einstein manifold
• riemannian curvature tensor