In this paper, we study the nature of Lorentzian α-Sasakian manifolds admitting M-projective curvature tensor. We show that M-projectively flat and irrotational M-projective curvature tensor of Lorentzian α-Sasakian manifolds are locally isometric to unit sphere Sn(c) , where c = α2. Next we study Lorentzian α-Sasakian manifold with conservative M-projective curvature tensor. Finally, we find certain geometrical results if the Lorentzian α-Sasakian manifold satisfying the relation M(X,Y)⋅R=0.
International Journal of Pure Mathematical Sciences (Volume 18)
D.G. Prakasha and V. Chavan, "On M-Projective Curvature Tensor of Lorentzian α-Sasakian Manifolds", International Journal of Pure Mathematical Sciences, Vol. 18, pp. 22-31, 2017