Bach-flat gradient steady Ricci solitons
By Huaihuo Cao, G. Catino, Qiang Chen, Carlo Mantegazza, L. Mazzieri. Calculus of Variations and Partial Differential Equations, 2011
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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).
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3444dc88c473088ea924297207a303267fa2f84c
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Citations in the corpus
- Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature (2021, unknown): “Classification results have been obtained in [11] for Bach flat steady solitons in dimension n ≥ 4 under some conditions.”
- Bach-Flat Critical Metrics of the Volume Functional on 4-Dimensional Manifolds with Boundary (2014, background): “The first part of the proof will follow [9].”
- On the geometry of gradient einstein-type manifolds (2014, background): “As a consequence, in the case of gradient Ricci solitons, we recover a local version of the results in [8] and [6], while, in the cases of ρ-Einstein solitons and Ricci almost solitons, we prove two new classification theorems (see Theorem 9.”