On $(\epsilon )$-para Sasakian 3-manifolds

Abstract

In this paper we study the 3-dimensional $(\epsilon )$-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\epsilon )$-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric $(\epsilon )$-para Sasakian 3 -manifold is an indefinite space form. We investigate the necessary and sufficient condition for an $(\epsilon )$-para Sasakian 3 -manifold to be locally $\phi$-symmetric. It is proved that in an $(\epsilon )$-para Sasakian 3-manifold with $\eta$ -parallel Ricci tensor the scalar curvature is constant. It is also shown that every $(\epsilon )$-para Sasakian 3-manifolds is pseudosymmetric in the sense of R. Deszcz.

12 pages