Einstein doubly warped product manifolds with a semi-symmetric metric connection

TL;DR

This paper investigates the geometric properties of doubly warped product manifolds with semi-symmetric metric connections, deriving curvature formulas and conditions for Einstein-like structures, advancing understanding in differential geometry.

Contribution

It introduces curvature formulas and conditions for Einstein and Einstein-like structures in doubly warped product manifolds with semi-symmetric metric connections, extending previous geometric frameworks.

Findings

Derived curvature formulas in terms of component curvatures.

Established necessary and sufficient conditions for warped product structures.

Identified criteria for Einstein and Einstein-like doubly warped product manifolds.

Abstract

In this paper, we study the doubly warped product manifolds with semisymmetric metric connection. We derive the curvatures formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of components of doubly warped product manifolds. We also prove the necessary and sufficient condition for a doubly warped product manifold to be a warped product manifold. We obtain some results for Einstein doubly warped product manifold and Einstein-like doubly warped product manifold of class A with respect to a semi-symmetric metric connection.