Study on Einstein Warped Product space with Quarter Symmetric Connection

TL;DR

This paper investigates Einstein warped spaces equipped with a quarter symmetric connection, deriving curvature properties and conditions under which such spaces simplify to Riemannian products, especially with nonpositive scalar curvature.

Contribution

It introduces new results on curvature tensors for Einstein warped spaces with quarter symmetric connections and characterizes when these spaces reduce to Riemannian products.

Findings

Derived curvature, Ricci, and scalar tensor formulas for quarter symmetric connections.

Proved conditions under which Einstein warped spaces become Riemannian products.

Established results for spaces with nonpositive scalar curvature and compact base.

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.