Volume 3, issue 1 (1999)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
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