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Developments around positive sectional curvature
Karsten Grove
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. I…
Lifting Group Actions and Nonnegative Curvature
Karsten Grove, Wolfgang Ziller
We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric o…
Symmetries of Eschenburg spaces and the Chern problem
Karsten Grove, Krishnan Shankar, Wolfgang Ziller
The known manifolds of positive sectional curvature are either homogeneous spaces or biquotients, i.e. quotients of a compact Lie group by a group acting on the left and right simu…
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres
K. Grove, B. Wilking, L. Verdiani +1
In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds, that do not support invariant metrics of non-negative sectional curvature. In fact…