Examples of Riemannian manifolds with positive curvature almost everywhere

Petersen, Peter¹ ; Wilhelm, Frederick²

¹ Department of Mathematics, University of California, Los Angeles, California 90095, USA
² Department of Mathematics, University of California, Riverside, California 92521-0135, USA

Geometry & topology, Tome 3 (1999) no. 1, pp. 331-367.

Résumé

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.

Détail

DOI : 10.2140/gt.1999.3.331

Keywords: positive curvature, unit tangent bundle of $S^4$

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