Rigidity theorem for integral pinched shrinking Ricci solitons

DOI10.1007/s00605-017-1042-1zbMath1372.53047arXiv1510.07121OpenAlexW2963781157MaRDI QIDQ2364425

Li-Qun Xiao, Hai-Ping Fu

Publication date: 20 July 2017

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07121

zbMATH Keywords

Einstein manifoldRicci solitonWeyl curvature tensorYamabe constant

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24)

Related Items (12)

Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds ⋮ Integral pinched gradient shrinking \(\rho\)-Einstein solitons ⋮ Integral pinching characterization of compact shrinking Ricci solitons ⋮ Some remarks on Bach-flat manifolds with positive constant scalar curvature ⋮ RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR ⋮ Rigidity of complete noncompact Riemannian manifolds with harmonic curvature ⋮ On compact manifolds with harmonic curvature and positive scalar curvature ⋮ Some \(L^p\) rigidity results for complete manifolds with harmonic curvature ⋮ Four-manifolds with positive Yamabe constant ⋮ Rigidity of Riemannian manifolds with positive scalar curvature ⋮ On critical point equation of compact manifolds with zero radial Weyl curvature ⋮ Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds

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• Ricci solitons on compact three-manifolds
• Positively curved shrinking Ricci solitons are compact
• Positive Einstein metrics with small \(L^{n/2}\)-norm of the Weyl tensor
• Isolation of the Weyl conformal tensor for Einstein manifolds.
• Recent Progress on Ricci Solitons
• The Yamabe problem

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