Volume 3, issue 1 (1999)

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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 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.

Keywords
positive curvature, unit tangent bundle of $S^4$
Mathematical Subject Classification
Primary: 53C20
Secondary: 53C20, 58B20, 58G30
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Publication
Received: 27 March 1999
Revised: 30 July 1999
Accepted: 6 October 1999
Published: 14 October 1999
Proposed: Steve Ferry
Seconded: Gang Tian, Walter Neumann
Authors
Peter Petersen
Department of Mathematics
University of California
Los Angeles
California 90095
USA
Frederick Wilhelm
Department of Mathematics
University of California
Riverside
California 92521-0135
USA