An exotic sphere with positive curvature almost everywhere.

DOI10.1007/BF02922018zbMath1039.53037OpenAlexW1971264745MaRDI QIDQ1608505

Frederick H. jun. Wilhelm

Publication date: 8 August 2002

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922018

zbMATH Keywords

positive curvatureexotic sphere

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Differentiable structures in differential topology (57R55) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (20)

Relations between metrics of almost positive curvature on the Gromoll-Meyer sphere ⋮ Rationally 4-periodic biquotients ⋮ The classification of \(\mathrm{SU}(2)^2\) biquotients of rank 3 Lie groups ⋮ Some new examples with almost positive curvature ⋮ On the Hopf conjecture with symmetry ⋮ Almost positive curvature on the Gromoll-Meyer sphere ⋮ Exotic spheres and curvature ⋮ The weighted connection and sectional curvature for manifolds with density ⋮ A note on quasi-positive curvature conditions ⋮ The classification and curvature of biquotients of the form \(\mathrm{Sp}(3)//\mathrm{Sp}(1)^2\) ⋮ On the curvature of biquotients ⋮ Quasipositive curvature on a biquotient of \(\mathrm{Sp}(3)\) ⋮ The diffeomorphism type of certain 𝑆³-bundles over 𝑆⁴ ⋮ Almost positive curvature on the Gromoll-Meyer 7-sphere ⋮ Three new almost positively curved manifolds ⋮ A characterization of affine hyperquadrics ⋮ Curvature, Sphere Theorems, and the Ricci flow ⋮ A minimal Brieskorn 5-sphere in the Gromoll-Meyer sphere and its applications ⋮ Examples of Riemannian manifolds with positive curvature almost everywhere ⋮ A Note on Maximal Symmetry Rank, Quasipositive Curvature, and Low Dimensional Manifolds

Cites Work

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• A proof of the Smale conjecture, \(Diff(S^ 3)\simeq O(4)\)
• An exotic sphere with nonnegative sectional curvature
• Examples of Riemannian manifolds with positive curvature almost everywhere
• Curvature increasing metric variations
• Some examples of manifolds of nonnegative curvature
• The fundamental equations of a submersion
• Quelques variations particulières d'un produit de métriques
• Exotic spheres with lots of positive curvatures

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