Quasi-Einstein and Generalized Quasi-Einstein Warped Products with an Affine Connection

TL;DR

This paper investigates the properties of quasi-Einstein and generalized quasi-Einstein warped products equipped with a semi-symmetric non-metric connection, deriving Ricci tensors and scalar curvatures, and identifying conditions that hinder their existence.

Contribution

It provides explicit formulas for Ricci tensors and scalar curvatures in this context and establishes obstructions to the existence of such warped products.

Findings

Derived Ricci tensor expressions for the warped products.

Calculated scalar curvatures for bases and fibers.

Identified conditions preventing the existence of these structures.

Abstract

In this paper, we study the quasi-Einstein and generalized quasi-Einstein warped products with a semi-symmetric non-metric connection. We give the expressions of the Ricci tensors and scalar curvatures for the bases and fibres. In some cases we give some obstructions to the existence of the quasi-Einstein and generalized quasi-Einstein warped products with a semi-symmetric non-metric connection.