In this paper, we study Einstein warped product space with respect to semi symmetric metric connection. During establish some results on curvature, Ricci and scalar tensors connection second order the last section, investigate under what conditions, if $M$ is an nonpositive curvature compact base then simply a Riemannian space.

In this paper we introduce notion of Ricci solitons in -para Kenmotsu manifold with semi -symmetric metric connection. We have found the relations between curvature tensor, tensors and scalar semi-symmetic connection.We proved that 3-dimensional connection is an -Einstein soliton defined on named expanding steady respect to value constant.It Conharmonically flat semi-symmetric manifold.

given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...

Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most homogeneous case. In this direction, famous ones are results by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov other At same time, studying little for case an arbitrary metri...

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...