On lorentzian α-sasakian manifolds

Abstract

The present paper deals with Lorentzian alpha-Sasakian manifolds with conformally flat and quasi conformally flat curvature tensor. It is shown that in both cases, the manifold is locally isometric with a sphere S-2n + 1 (c). Further it is shown that an Lorentzian alpha-Sasakian manifold with R (X; Y):C = 0 is locally isometric with a sphere S-2n + 1 (c), where c = alpha(2).