We provide an exhaustive description of all simply connected positively curved
cohomogeneity one manifolds. The description yields a complete classification in all …

Manifolds with non-negative sectional curvature have been of interest since the beginning of
global Riemannian geometry, as illustrated by the theorems of Bonnet-Myers, Synge, and …

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A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold
with positive sectional curvature has positive Euler characteristic. We prove this conjecture …

As a means to better understanding manifolds with positive curvature, there has been much
recent interest in the study of non-negatively curved manifolds which contain either a point …

We discuss manifolds with positive sectimal curvature on which a group acts isometrically
with one dimensional quotient. A number of the known examples have this property, but …

We examine topological properties of the seven-dimensional positively curved Eschenburg
biquotients and find many examples which are homeomorphic but not diffeomorphic. A …

Most of the few known examples of compact Riemannian manifolds with positive sectional
curvature are the total space of a Riemannian submersion. In this article we show that this is …

We investigate the curvature of Eschenburg spaces with respect to two different metrics, one
constructed by Eschenburg and the other by Wilking. With respect to the Eschenburg metric …

We study the sectional curvature of all of the cohomogeneity two Bazaikin spaces with
respect to a Riemannian metric construction due to Wilking. We show that, in contrast to the …