On the structure of conformally flat Riemannian manifolds

DOI10.1016/j.na.2015.05.001zbMath1326.53047OpenAlexW224045886WikidataQ115342956 ScholiaQ115342956MaRDI QIDQ491646

He-Zi Lin

Publication date: 18 August 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.05.001

zbMATH Keywords

endsconformally flatvanishing theorems\(L^2\)-harmonic 1-forms

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20)

Related Items (10)

Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds ⋮ Geometries and topologies of conformally flat Riemannian manifolds ⋮ \(L^2\) curvature pinching theorems and vanishing theorems on complete Riemannian manifolds ⋮ Vanishing theorems for \(p\)-harmonic forms on Riemannian manifolds ⋮ Scalar curvature and Betti numbers of compact Riemannian manifolds ⋮ Vanishing theorems for Riemannian manifolds with nonnegative scalar curvature and weighted \(p\)-Poincaré inequality ⋮ Unnamed Item ⋮ The topological structure of conformally flat Riemannian manifolds ⋮ Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature ⋮ \(L^p\) harmonic 1-forms on conformally flat Riemannian manifolds

Cites Work

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• An exact sequence in \(L^2\)-cohomology
• Schouten curvature functions on locally conformally flat Riemannian manifolds
• COMPACT LOCALLY CONFORMALLY FLAT RIEMANNIAN MANIFOLDS
• Some characterizations of space-forms
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• An Application of Yau's Maximum Principle to Conformally Flat Spaces
• On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
• Conformally Flat Manifolds and a Pinching Problem on the Ricci Tensor

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