Some curvature properties of $(κ, \mu)$ contact space forms

Abstract

The object of the present paper is to find Ricci tensor of $(k, \mu)$ space forms. In particular we prove that a three dimensional $(k, \mu)$ space forms is $\eta$-Einstein for $\mu=\frac{1}{2}$. We also study three dimensional $(k, \mu)$ space forms with $\eta$- parallel and cyclic parallel Ricci tensor for $\mu=\frac{1}{2}$. We also prove that every $(k, \mu)$ space forms is locally $\phi$- symmetric.