Structure of generalized Yamabe solitons and its applications

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...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2024-05, Vol.67 (2), p.336-348
Main Author: Maeta, Shun
Format: Article
Language:English
Subjects:
Solitary waves
Theorems
Citations: Items that this one cites
Online Access:Get full text
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Summary: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.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091524000117