Bach-flat gradient steady Ricci solitons
In this paper we prove that any n -dimensional ( n ≥ 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric...
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Published in | Calculus of variations and partial differential equations Vol. 49; no. 1-2; pp. 125 - 138 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
2014
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | In this paper we prove that any
n
-dimensional (
n
≥ 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in Cao and Chen (Trans Am Math Soc 364:2377–2391,
2012
) and Catino and Mantegazza (Ann Inst Fourier 61(4):1407–1435,
2011
). |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0944-2669 1432-0835 |
DOI: | 10.1007/s00526-012-0575-3 |