Some curvature properties of Lorentzian α-Sasakian manifolds

Abstract

Abstract The object of the present paper is to study the pseudo-projective φ-recurrent and generalized projective recurrent Lorentzian α-Sasakian manifolds. Here we show that pseudo-projective φ-recurrent Lorentzian α-Sasakian Manifold is an Einstein manifold and in the case of generalized projective φ- recurrent Lorentzian α-Sasakian manifold, we find a relation between the associated 1-forms A and B. We have also proved that the characteristic vector field ξ and vector field ρ associated to the 1-forms A and B are co-directional. We also study quasi-projectively flat Lorentzian α-Sasakian manifolds.