Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature
By Fengjiang Li. 2021
48 citations recorded by the source corpus.
Our main aim in this paper is to investigate the rigidity of complete noncompact gradient steady Ricci solitons with harmonic Weyl tensor. More precisely, we prove that an $n$-dimensional ($n\geq 5$) complete noncompact gradient steady Ricci soliton with harmonic Weyl tensor and multiply warped product metric is either Ricci flat or isometric to the Bryant soliton up to scaling. Meanwhile, for $n\ge 5$, we provide a local structure theorem for $n$-dimensional connected (not necessarily complete) gradient Ricci solitons with harmonic Weyl curvature and multiply warped product metric.
View Paper: https://www.semanticscholar.org/paper/2c87a5a4785a9f265e746bdd82d48e8f2460ae9d
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Citations in the corpus
- Entanglement islands in higher dimensions (2019, background): “It can be shown that DeTurck solitons do not exist for static and certain stationary solutions of (11) with purely Dirichlet boundaries [35, 36].”