On Three Dimensional (?) - Lorentzian Para ? Sasakian Manifolds

Gyanvendra Pratap Singh, Sunil Kumar Srivastava, Marutosh Pathak

Abstract: The object of the present paper is to study three dimensional () -Lorentzian Para Sasakian Manifolds. We discussed about an () - Lorentzian Para Sasakian 3-Manifold to be an indefinite space form and get necessary and sufficient condition. Also shown that Ricci semi-symmetric () - Lorentzian Para Sasakian 3-Manifold is an indefinite space form. we investigate the necessary and sufficient condition for an () - Lorentzian Para Sasakian 3-Manifold to be locally -symmetric. We have also proved that in a three- dimensional () - Lorentzian Para Sasakian manifolds with - parallel Ricci tensor the scalar curvature is constant, Finally we give an example of () - Lorentzian Para Sasakian manifolds which verify all results

Keywords: Lorentzian Para Sasakian 3 Manifolds, Ricci, semi symmetric space, locally symmetric space, parallel Ricci tensor