The Differentiable Sphere Theorem (After S. Brendle and R. Schoen)

DOI10.1007/978-3-319-42351-7_1zbMath1406.53040OpenAlexW2512310050MaRDI QIDQ4645256

Gérard Besson

Publication date: 10 January 2019

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-42351-7_1

zbMATH Keywords

curvature tensorRiemannian manifoldcurvature operatorsectional curvatureirreducible component

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Cites Work

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• Classification of manifolds with weakly 1/4-pinched curvatures
• A general convergence result for the Ricci flow in higher dimensions
• Manifolds with nonnegative isotropic curvature
• Ricci deformation of the metric on a Riemannian manifold
• Four-manifolds with positive curvature operator
• Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes
• A sharp characterization of the smooth 4-sphere in curvature terms
• Sur les variétés riemanniennes pincées juste au-dessous de 1/4
• Negatively \(1\over 4\)-pinched Riemannian metric on a compact Kähler manifold
• Pointwise 1/4-pinched 4-manifolds
• Metrics with nonnegative isotropic curvature
• Fundamental groups of manifolds with positive isotropic curvature
• Three-manifolds with positive Ricci curvature
• Kähler manifolds and 1/4-pinching
• Manifolds with positive curvature operators are space forms
• Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung
• Ricci flow with surgery on four-manifolds with positive isotropic curvature
• The fundamental group of manifolds of positive isotropic curvature and surface groups
• A contribution to differential geometry in the large
• Einstein manifolds with nonnegative isotropic curvature are locally symmetric
• Manifolds with 1/4-pinched curvature are space forms
• Sur quelques variétés riemanniennes suffisamment pincées
• On the topology of manifolds with positive isotropic curvature
• Classification of almost quarter-pinched manifolds
• A Panoramic View of Riemannian Geometry
• A Compactness Property for Solutions of the Ricci Flow
• Isotropic Curvature and the Ricci Flow
• Four-manifolds with positive isotropic curvature
• Riemannian geometry