Paper · Aug 14, 2020
Remarks on almost Riemann solitons with gradient or torse-forming vector field
As on arXiv
Abstract
We consider almost Riemann solitons in a Riemannian manifold and underline their relation to almost Ricci solitons. When is of gradient type, using Bochner formula, we explicitly express the function by means of the gradient vector field and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential vector field of the soliton is solenoidal or torse-forming, with a special view towards curvature.
- Submitted
- Aug 14, 2020
- Last revised
- Jan 15, 2021 (v4)
- Subjects
- math.DG
- Journal
- Bulletin of the Malaysian Mathematical Sciences Society 44, 3215-3227 (2021)
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Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.