Paper · Dec 24, 2020
On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor
As on arXiv
Abstract
In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify -dimensional () complete -flat gradient steady Ricci solitons. More precisely, we prove that any -dimensional complete noncompact gradient steady Ricci soliton with vanishing -tensor is either Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof extends to the shrinking case and the expanding case as well.
- Submitted
- Dec 24, 2020
- Last revised
- Jan 23, 2021 (v2)
- Subjects
- math.DG
- Journal
- Proc. Amer. Math. Soc. 149 (2021), no. 4, 1733-1742
Comments: 10 pages; final version to appear in Proc. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:1105.3163
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Background reading
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In the guidebook
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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.
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Comparing curvature across space and time.
- 12B.1κ-Solutions
Ancient, nonnegatively curved, noncollapsed: the models for singularities.