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On complete gradient steady Ricci solitons with vanishing 𝐷-tensor
- Source :
- Proceedings of the American Mathematical Society. 149:1733-1742
- Publication Year :
- 2021
- Publisher :
- American Mathematical Society (AMS), 2021.
-
Abstract
- In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat gradient steady Ricci solitons. More precisely, we prove that any $n$-dimensional complete noncompact gradient steady Ricci soliton with vanishing $D$-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.<br />10 pages; final version to appear in Proc. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:1105.3163
- Subjects :
- Mathematics - Differential Geometry
Work (thermodynamics)
Applied Mathematics
General Mathematics
MathematicsofComputing_GENERAL
53C21
Ricci soliton
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Differential Geometry (math.DG)
FOS: Mathematics
Mathematics::Metric Geometry
Mathematics::Differential Geometry
Soliton
Tensor
Nonlinear Sciences::Pattern Formation and Solitons
Mathematics
Mathematical physics
Subjects
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 149
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....da17c76739ebabf5b2295916e82cd05a