Kenmotsu Pseudo-Riemannian Manifolds

In this paper, we give some fundamental definitions and concepts of almost contact manifolds.We study some properties of Kenmotsu manifolds with pseudo-Riemannian metrics. We prove that this kind of manifolds satisfying certain conditions such as R(X, Y)-R=0, R(X, Y)·S=0 are Einstein manifolds. Also we s-tudy some conditions related to M-projectively tensor. These conditions are: M-projectively flat; M-projective curvature tensor and concircular curvature tensor, con-harmonic curvature tensor, conformal curvature tensor are lin-early dependent.