Curvature of multiply warped products with an affine connection

TL;DR

This paper investigates the geometric properties of multiply warped product manifolds with semi-symmetric non-metric and affine connections, focusing on Einstein conditions and constant scalar curvature, and provides new examples of affine manifolds.

Contribution

It introduces new results on Einstein and scalar curvature conditions for multiply warped products with semi-symmetric non-metric and affine connections, including applications to specific spacetimes.

Findings

Derived conditions for Einstein multiply warped products with semi-symmetric non-metric connections.

Constructed new examples of Einstein affine manifolds.

Analyzed scalar curvature properties in generalized Robertson-Walker and Kasner spacetimes.

Abstract

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifolds with constant scalar curvature.{\ss} We also consider the multiply warped products with an affine connection with a zero torsion.