Some results on lorentzian α-sasakian manifolds

Abstract

The purpose of this work is to introduce Lorentzian -Sasakian manifolds to the concept of an extended -curvature tensor. This study’s findings include the demonstration of an extended Lorentzian -Sasakian manifold that satisfies certain requirements for the -curvature tensor. First we demonstrated that, it is local isometric to the hyperbolic space because a Lorentzian -Sasakian manifold satisfying  is a space with constant curvature .  Further, we proved that, Einstein manifolds are -semisymmetric Lorentzian -Sasakian  manifolds. Additionally we validated that, the hyperbolic space is locally isometric to a -semisymmetric Lorentzian -Sasakian manifold, that is a space with constant curvature of . Additionally, we gathered data on an Einstein manifold is a  that is a  satisfying Lorentzian -Sasakian manifold, a  Lorentzian -Sasak manifold that satisfies the  condition is an Einstein manifold and Einstein manifolds are Lorentzian -Sasakian manifolds that meet the equation .