#### Volume 3, issue 1 (1999)

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Examples of Riemannian manifolds with positive curvature almost everywhere

### Peter Petersen and Frederick Wilhelm

Geometry & Topology 3 (1999) 331–367
 arXiv: math.DG/9910187
##### Abstract

We show that the unit tangent bundle of ${S}^{4}$ and a real cohomology $ℂ{P}^{3}$ 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.

##### Keywords
positive curvature, unit tangent bundle of $S^4$
##### Mathematical Subject Classification
Primary: 53C20
Secondary: 53C20, 58B20, 58G30