Positive Einstein metrics with small \(L^{n/2}\)-norm of the Weyl tensor

DOI10.1016/0926-2245(92)90014-EzbMath0741.53035WikidataQ115362750 ScholiaQ115362750MaRDI QIDQ1813065

Michael A. Singer

Publication date: 25 June 1992

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

Euler characteristicWeyl tensorEinstein metricYang-Mills fieldsgap theoremSobolev constant\(L^ p\)-norm

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07)

Related Items (17)

Rigidity theorem for integral pinched shrinking Ricci solitons ⋮ 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 ⋮ A sphere theorem for Bach-flat manifolds with positive constant scalar 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 ⋮ Rigidity of noncompact complete manifolds with harmonic curvature ⋮ An inequality between Willmore functional and Weyl functional for submanifolds in space forms ⋮ On the isolation phenomena of Einstein manifolds—submanifolds versions ⋮ Isolation of the Weyl conformal tensor for Einstein manifolds.

Cites Work

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• A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
• Some isoperimetric inequalities and eigenvalue estimates
• On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
• Characteristic Classes. (AM-76)

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