A rigidity theorem for complete noncompact Bach-flat manifolds

DOI10.1016/j.geomphys.2010.11.003zbMath1210.53048OpenAlexW1965176377MaRDI QIDQ629387

Yawei Chu

Publication date: 9 March 2011

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2010.11.003

zbMATH Keywords

space formBach-flattrace-free curvature tensor

Mathematics Subject Classification ID

Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (7)

Rigidity theorem for compact Bach-flat manifolds with positive constant \(\sigma_2\) ⋮ Universal curvature identities. II. ⋮ Unnamed Item ⋮ Rigidity of complete noncompact bach-flat \(n\)-manifolds ⋮ RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR ⋮ Rigidity of complete noncompact Riemannian manifolds with harmonic curvature ⋮ Complete noncompact manifolds with harmonic curvature

Cites Work

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• Rigidity of noncompact complete Bach-flat manifolds
• Ambient metrics for \(n\)-dimensional \(pp\)-waves
• Intrinsic geometry of oriented congruences in three dimensions
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Ricci deformation of the metric on a Riemannian manifold
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Bach-flat asymptotically locally Euclidean metrics
• On a conformal gap and finiteness theorem for a class of four-manifolds
• Obstructions to conformally Einstein metrics in \(n\) dimensions
• Asymptotic curvature decay and removal of singularities of Bach-flat metrics
• The normal conformal Cartan connection and the Bach tensor

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