Structure of generalized Yamabe solitons and its applications

TL;DR

This paper explores the structure of conformal gradient Yamabe solitons, providing new insights and partial solutions to related conjectures, thereby advancing the understanding of Yamabe solitons in geometric analysis.

Contribution

It characterizes the structure of complete gradient conformal solitons and offers partial answers to the Yamabe soliton version of Perelman's conjecture.

Findings

Elucidation of the structure of complete gradient conformal solitons.

Applications to gradient Yamabe solitons.

Partial affirmative answer to Perelman's conjecture for Yamabe solitons.

Abstract

We consider the broadest concept of the gradient Yamabe soliton, the conformal gradient soliton. In this paper, we elucidate the structure of complete gradient conformal solitons under some assumption, and provide some applications to gradient Yamabe solitons. These results enhance the understanding gained from previous research. Furthermore, we give an affirmative partial answer to the Yamabe soliton version of Perelman's conjecture.