Some results on LP-Sasakian manifolds

Abstract

The object of the present paper is to characterize LP-Sasakian manifolds satisfying Ricci pseudosymmetry and Ricci generalized pseudosymmetry. Beside this we prove that if R(X; ξ): P = P(X; ξ): R holds, where R and P denote the curvature tensor and projective curvature tensor respectively, then the manifold becomes an Einstein manifold. Then we prove that divR = 0 and divC = 0 are equivalent if the scalar curvature is invariant under the characteristic vector field ξ, where 'div' denotes divergence. Finally, we characterize 3-dimensional LP-Sasakian manifolds admitting Yamabe solitons and prove that the scalar curvature is constant and the potential vector field V is Killing.