Geometry & Topology

Examples of Riemannian manifolds with positive curvature almost everywhere

Peter Petersen and Frederick Wilhelm

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We show that the unit tangent bundle of S4 and a real cohomology P3 admit Riemannian metrics with positive sectional curvature almost everywhere. These are the only examples so far with positive curvature almost everywhere that are not also known to admit positive curvature.

Article information

Geom. Topol., Volume 3, Number 1 (1999), 331-367.

Received: 27 March 1999
Revised: 30 July 1999
Accepted: 6 October 1999
First available in Project Euclid: 21 December 2017

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Zentralblatt MATH identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 58B20: Riemannian, Finsler and other geometric structures [See also 53C20, 53C60] 58G30

positive curvature unit tangent bundle of $S^4$


Petersen, Peter; Wilhelm, Frederick. Examples of Riemannian manifolds with positive curvature almost everywhere. Geom. Topol. 3 (1999), no. 1, 331--367. doi:10.2140/gt.1999.3.331.

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