Isolation of the Weyl conformal tensor for Einstein manifolds.

DOI10.3792/pjaa.78.140zbMath1033.53038OpenAlexW2089792705MaRDI QIDQ1869654

Mitsuhiro Itoh, Hiroyasu Satoh

Publication date: 22 March 2004

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.78.140

zbMATH Keywords

Einstein manifoldsSobolev inequalityWeyl conformal tensorYamabe metric

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25)

Related Items (17)

Rigidity theorem for integral pinched shrinking Ricci solitons ⋮ Rigidity theorems of complete Kähler-Einstein manifolds and complex space forms ⋮ Einstein manifolds with finite \(L^p\)-norm of the Weyl curvature ⋮ Rigidity theorem for compact Bach-flat manifolds with positive constant \(\sigma_2\) ⋮ On closed manifolds with harmonic Weyl curvature ⋮ On compact Riemannian manifolds with harmonic Weyl curvature ⋮ Some remarks on Bach-flat manifolds with positive constant scalar curvature ⋮ \(L^{n/2}\)-curvature gaps of the Weyl tensor ⋮ Almost conformally flat hypersurfaces ⋮ Rigidity theorems for complete Sasakian manifolds with constant pseudo-Hermitian scalar curvature ⋮ On compact manifolds with harmonic curvature and positive scalar curvature ⋮ Some \(L^p\) rigidity results for complete manifolds with harmonic curvature ⋮ Rigidity of noncompact complete Bach-flat manifolds ⋮ On the stability of Einstein manifolds ⋮ Rigidity of noncompact complete manifolds with harmonic curvature ⋮ On the geometry of \(\varphi\)-curvatures ⋮ On the isolation phenomena of Einstein manifolds—submanifolds versions

Cites Work

• Unnamed Item
• Yamabe metrics of positive scalar curvature and conformally flat manifolds
• Four-manifolds with \(\delta W^+=0\) and Einstein constants of the sphere.
• Positive Einstein metrics with small \(L^{n/2}\)-norm of the Weyl tensor
• The Yamabe problem
• YAMABE METRICS AND THE SPACE OF CONFORMAL STRUCTURES
• The WeitzenbÕck formula for the Bach operator

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