As on arXiv
Abstract
We consider gradient Ricci solitons conformal to a -dimensional pseudo-Euclidean space and we completely describe the most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary differential equations. As a consequence, the gradient Ricci solitons that arise from the reduced system are invariant under the action of either an -dimensional translation group or the pseudo-orthogonal group acting on the corresponding -dimensional pseudo-Euclidean space.
- Submitted
- May 10, 2018
- Last revised
- May 14, 2018 (v2)
- Subjects
- math.DG
- Journal
- Annales Academiae Scientiarum Fennicae 2020
Its neighbourhood
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The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.
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Ricci solitons on low-dimensional generalized symmetric spaces
Topics Ricci solitons · Shared terms “dimensional pseudo”, “differential equation”, “partial differential”
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The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
Topics Ricci solitons · Same author João Paulo dos Santos · Shared terms “gradient Ricci”
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Topics Ricci solitons · Shared terms “dimensional pseudo”, “gradient Ricci”
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Topics Ricci solitons · Same author Benedito Leandro · Shared terms “gradient Ricci”
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Topics Ricci solitons · Shared terms “dimensional translation”, “translation group”, “gradient Ricci”
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Local structure of gradient almost Ricci solitons with harmonic Weyl tensor
Topics Ricci solitons · Same author João Paulo dos Santos
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Topics Ricci solitons · Same author João Paulo dos Santos
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.