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...

As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its LeviCivita connection? It is shown that for a generic Levi-Civita connection of a metric h there exists a set of positive semi-defi...

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.

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.