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Some results on Ricci-Bourguignon solitons and almost solitons

Part of: Global differential geometry

Published online by Cambridge University Press:  20 August 2020

Shubham Dwivedi
Shubham Dwivedi*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
*
e-mail: s2dwived@uwaterloo.ca
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Abstract

We prove some results for the solitons of the Ricci–Bourguignon flow, generalizing the corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci–Bourguignon almost solitons and prove some results about them that generalize previous results for Ricci almost solitons. We also derive integral formulas for compact gradient Ricci–Bourguignon solitons and compact gradient Ricci–Bourguignon almost solitons. Finally, using the integral formula, we show that a compact gradient Ricci–Bourguignon almost soliton is isometric to a Euclidean sphere if it has constant scalar curvature or its associated vector field is conformal.

Keywords

Ricci–Bourguignon flowsolitonsalmost solitonsself-similar solutions

MSC classification

Secondary: 53C20: Global Riemannian geometry, including pinching 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 3 , September 2021 , pp. 591 - 604
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Copyright
© Canadian Mathematical Society 2020

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