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Structure of generalized Yamabe solitons and its applications

Part of: Global differential geometry

Published online by Cambridge University Press:  07 March 2024

Shun Maeta Open the ORCID record for Shun Maeta [Opens in a new window]
Shun Maeta*
Affiliation:
Department of Mathematics, Faculty of Education, Chiba University, Chiba-shi, Chiba, Japan Department of Mathematics and Informatics, Graduate School of Science and Engineering, Chiba University, Chiba-shi, Chiba, Japan (shun.maeta@gmail.com)
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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.

Keywords

Yamabe solitonsYamabe flowk-Yamabe solitonsconformal gradient solitons

MSC classification

Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C20: Global Riemannian geometry, including pinching
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 13
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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