Examples of Riemannian manifolds with positive curvature almost everywhere

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.

arXiv comment37 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper14.abs.html

Cited by in corpus (8)

• The classification of compact simply connected biquotients in dimension 6 and 7
• Some new examples with almost positive curvature
• On the curvature of biquotients
• How to lift positive Ricci curvature
• The classification of compact simply connected biquotients in dimension 4 and 5
• The classification and curvature of biquotients of the form $Sp(3)//Sp(1{)}^2$
• Quasi-positive curvature on a biquotient of $Sp(3)$
• The classification of $SU(2{)}^2$ biquotients of rank $3$ Lie groups