Study on Einstein Warped Product space with Quarter Symmetric Connection

Abstract

We study Einstein warped space with a quarter symmetric connection. As a result, first, we find basic results on curvature, Ricci and scalar tensors with respect to the quarter symmetric connection. Moreover, we prove some results corresponding to second order quarter symmetric connection. Finally, we prove that if $M$ is an Einstein warped space with nonpositive scalar curvature and compact base with respect to quarter symmetric connection and the warping function satisfy some condition then $M$ is simply a Riemannian product space.