Rigid properties for gradient generalized \(m\)-quasi-Einstein manifolds and gradient shrinking Ricci solitons

DOI10.1016/j.jmaa.2022.126702zbMath1504.53065OpenAlexW4296645165MaRDI QIDQ2091016

Deng YiHua

Publication date: 31 October 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2022.126702

zbMATH Keywords

rigidityshrinking Ricci solitonWeyl curvaturegradient generalized \(m\)-quasi-Einstein manifolds

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Ricci flows (53E20)

Cites Work

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• Generalized quasi-Einstein manifolds with harmonic Weyl tensor
• Rigidity of noncompact complete manifolds with harmonic curvature
• On complete gradient shrinking Ricci solitons
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• Characterizations and integral formulae for generalized \(m\)-quasi-Einstein metrics
• Strong uniqueness of the Ricci flow
• Ricci deformation of the metric on a Riemannian manifold
• Gradient shrinking Ricci solitons of half harmonic Weyl curvature
• Complete gradient shrinking Ricci solitons with pinched curvature
• Conformal diffeomorphisms of gradient Ricci solitons and generalized quasi-Einstein manifolds
• Some characterizations for compact almost Ricci solitons
• Rigid properties of quasi-Einstein metrics
• A theorem on Riemannian manifolds of positive curvature operator
• RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR

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