Volume 15, issue 1 (2011)

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Some new examples with almost positive curvature

Martin Kerin

Geometry & Topology 15 (2011) 217–260
Abstract

As a means to better understanding manifolds with positive curvature, there has been much recent interest in the study of nonnegatively curved manifolds which contain points at which all $2$–planes have positive curvature. We show that there are generalisations of the well-known Eschenburg spaces and quotients of ${S}^{7}×{S}^{7}$ which admit metrics with this property.

Keywords
biquotient, positive curvature, Pontrjagin class
Mathematical Subject Classification 2000
Primary: 53C20
Secondary: 57S25, 57T15