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

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

2009-11-25

arxiv.org/abs/0911.4786v2

Mathematics

Differential Geometry

12 pages

Scientific paper

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 $\varphi $-symmetric. It is proved that in an $ (\varepsilon) $-para Sasakian 3-manifold with $\eta $ -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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