Examples of Riemannian manifolds with positive curvature almost everywhere

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

References

Forward citations

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

Volume 3, issue 1 (1999)

Peter Petersen and Frederick Wilhelm