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

Ali Akbara,* and Avijit Sarkarb

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

Authors :

Ali Akbar^a,* and Avijit Sarkar^b

Author Address :

^a,bDepartment of Mathematics, University of Kalyani , Kalyani- 741235, West Bengal, India.

*Corresponding author.

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.

Keywords :

($k$, $mu $) contact space forms, $eta-$Einstein, $eta-$ parallel and cyclic parallel Ricci tensor, locally $phi-$ symmetric.

DOI :

Article Info :

Received : May 14, 2014; Accepted : October 15, 2014.