As on arXiv
Abstract
In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of gradient Ricci solitons that are realized as warped products, from which we know that the base spaces of these products are Ricci-Hessian type manifolds. We study this latter class of manifolds as the most appropriate setting to prove our results.
Comments: 12 pages
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Connected papers
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 2021, plus the canon.
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On a special class of gradient Ricci solitons
Topics Ricci solitons · Same authors José N. V. Gomes, Marcus A. M. Marrocos · Shared terms “warped metrics”, “gradient Ricci”, “realized”
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Gradient estimates for a parabolic partial differential equation under the Ricci-Bourguignon flow
Topics Rotational symmetry & warped products · Same author José N. V. Gomes
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Geometric properties of second Ricci solitons
Topics Rotational symmetry & warped products, Ricci solitons
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On the geometry of Riemannian warped product maps
Topics Rotational symmetry & warped products, Ricci solitons
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On noncompact warped product Ricci solitons
Topics Rotational symmetry & warped products, Ricci solitons · Shared terms “nonexistence”, “gradient Ricci”
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On Ricci solitons whose level hypersurfaces have parallel second fundamental form
Topics Rotational symmetry & warped products, Ricci solitons · Shared terms “gradient Ricci”
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Existence of singular rotationally symmetric gradient Ricci solitons in higher dimensions
Topics Rotational symmetry & warped products, Ricci solitons · Shared terms “gradient Ricci”
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Backward propagation of warped product structures and asymptotically conical shrinkers
Topics Rotational symmetry & warped products, Ricci solitons
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.