On Three Dimensional (?) - Lorentzian Para ? Sasakian Manifolds
Journal: International Journal of Science and Research (IJSR) (Vol.4, No. 12)Publication Date: 2015-12-05
Authors : Gyanvendra Pratap Singh; Sunil Kumar Srivastava; Marutosh Pathak;
Page : 2075-2078
Keywords : Lorentzian Para Sasakian 3 Manifolds; Ricci; semi symmetric space; locally symmetric space; parallel Ricci tensor;
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
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