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

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

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