On Einstein warped product space with respect to semi symmetric metric connection

Abstract

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