An exotic sphere with positive curvature almost everywhere.
type: Item
instance of: scholarly article
title: An exotic sphere with positive curvature almost everywhere.
zbMATH Open document ID: 1039.53037
DOI: 10.1007/BF02922018
published in: The Journal of Geometric Analysis
publication date: 2002-08-08T00:00:00Z
review text: Since Milnor's discovery of exotic spheres, an interesting problem in Riemannian geometry has been whether there are exotic spheres with positive curvature. The Gromoll-Meyer sphere gives an example of a nonnegatively curved exotic \(7\)-dimensional sphere [\textit{D. Gromoll}, and \textit{W. Meyer}, Ann. Math. (2) 100, 401--406 (1974; Zbl 0293.53015)]. This was the first example of an exotic sphere with such a property. In the present paper, the author shows that the Gromoll-Meyer metric has zero curvature on an open set of points. Moreover, the Gromoll-Meyer metric can be perturbed to one with positive curvature almost everywhere and admitting an effective \(SO(3)\)-action.
reviewed by: Sergio Console
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57R55
zbMATH DE Number: 1777180
zbMATH Keywords: exotic sphere
zbMATH Keywords: positive curvature
author: Frederick Wilhelm
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02922018
OpenAlex ID: W1971264745
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description: scientific article; zbMATH DE number 1777180