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On almost quotient Yamabe solitons

Part of: Global differential geometry

Published online by Cambridge University Press:  11 April 2024

Willian Tokura Open the ORCID record for Willian Tokura [Opens in a new window] ,
Marcelo Barboza Open the ORCID record for Marcelo Barboza [Opens in a new window] ,
Elismar Batista Open the ORCID record for Elismar Batista [Opens in a new window]  and
Priscila Kai Open the ORCID record for Priscila Kai [Opens in a new window]
Willian Tokura*
Affiliation:
Universidade Federal da Grande Dourados, FACET, Dourados – MS, 79825-070, Brazil
Marcelo Barboza
Affiliation:
Universidade Federal de Goiás, IME, Goiânia—GO, 74001–970, Brazil
Elismar Batista
Affiliation:
Instituto Federal do Tocantins, Campus Dianópolis, Tocantins—TO, 77.300-000, Brazil
Priscila Kai
Affiliation:
Universidade Federal de Goiás, IME, Goiânia—GO, 74001–970, Brazil
*
Corresponding author: Willian Tokura; Email: williantokura@ufgd.edu.br
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Abstract

In this paper, we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call almost quotient Yamabe solitons as they extend quite naturally those already called quotient Yamabe solitons. We present sufficient conditions for a compact almost quotient Yamabe soliton to be either trivial or isometric with an Euclidean sphere. We also characterize noncompact almost gradient quotient Yamabe solitons satisfying certain conditions on both its Ricci tensor and potential function.

Keywords

Almost quotient Yamabe solitonsYamabe solitonsσk-curvaturerigidity resultsnoncompact manifolds

MSC classification

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 15
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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