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- Title
Rigidity of four-dimensional gradient shrinking Ricci solitons.
- Authors
Cheng, Xu; Zhou, Detang
- Abstract
Let (M , g , f) be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation Ric + ∇ 2 f = λ g , where λ is a positive real number. We prove that if M has constant scalar curvature S = 2 λ , it must be a quotient of 핊 2 × ℝ 2 . Together with the known results, this implies that a four-dimensional complete gradient shrinking Ricci soliton has constant scalar curvature if and only if it is rigid, that is, it is either Einstein, or a finite quotient of Gaussian shrinking soliton ℝ 4 , 핊 2 × ℝ 2 or 핊 3 × ℝ .
- Subjects
EINSTEIN, Albert, 1879-1955; REAL numbers; CURVATURE; EINSTEIN manifolds
- Publication
Journal für die Reine und Angewandte Mathematik, 2023, Vol 2023, Issue 802, p255
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2023-0042