Gradient solitons on doubly warped product manifolds

TL;DR

This paper characterizes doubly warped product manifolds and explores various gradient solitons on them, analyzing their effects on factor manifolds and examining special curvature conditions like concircular and conharmonic flatness.

Contribution

It introduces new characterizations of doubly warped product manifolds and studies the behavior of different gradient solitons on these manifolds, including their impact on factor manifolds.

Findings

Gradient solitons influence the geometry of factor manifolds.

New characterizations for doubly warped product manifolds.

Conditions for concircularly and conharmonically flat cases.

Abstract

Firstly we provide new characterizations for doubly warped product manifolds. Then we consider several types of gradient solitons on them such as Riemann, Ricci, Yamabe and conformal and examine the effect of a gradient soliton on a doubly warped product to its factor manifolds. Finally we investigate the concircularly flat and conharmonically flat cases of doubly warped products.