Geometry & Topology, Vol. 3 (1999) Paper no. 14, pages 331--367.

Examples of Riemannian manifolds with positive curvature almost everywhere

Peter Petersen, Frederick Wilhelm

Abstract. We show that the unit tangent bundle of S^4 and a real cohomology CP^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

AMS subject classification. Primary: 53C20. Secondary: 53C20, 58B20, 58G30.

DOI: 10.2140/gt.1999.3.331

E-print: arXiv:math.DG/9910187

Submitted to GT on 27 March 1999. (Revised 30 July 1999.) Paper accepted 6 October 1999. Paper published 14 October 1999.

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Peter Petersen, Frederick Wilhelm
Department of Mathematics, University of California
Los Angeles, CA 90095, USA

Department of Mathematics,University of California
Riverside, CA 92521-0135, USA

Email: petersen@math.ucla.edu, fred@math.ucr.edu

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