On Warped Product Gradient Yamabe Soliton

TL;DR

This paper characterizes warped product gradient Yamabe solitons with specific symmetry and scalar conditions, providing explicit solutions and potential function characterizations, advancing understanding of geometric flows in pseudo-Euclidean contexts.

Contribution

It establishes necessary and sufficient conditions for warped product gradient Yamabe solitons with conformal base and scalar-constant fiber, including explicit solutions and potential function characterizations.

Findings

Derived conditions for warped product Yamabe solitons with conformal base.

Obtained explicit solutions in the steady, scalar-flat fiber case.

Characterized the potential function as separable variables.

Abstract

In this paper, we provide a necessary and sufficient conditions for the warped product $M=B\times_f F$ to be a gradient Yamabe soliton when the base is conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n-1)-dimensional translation group, and the fiber F is scalar-constant. As application, we obtain solutions in steady case with fiber scalar-flat. Besides, on the warped product we consider the potential function as separable variables and obtain some characterization of the base and the fiber.