Wolfgang Ziller
Published 2007-07-23Version 1
This is a survey on cohomogeneity one manifolds with positive curvature. We discuss the known examples of this type and their geometry and the functions that describe the metric. We also describe the classification of cohomogeneity one manifolds that can admit a metric with positive curvature due to Grove-Wilking-Ziller. Two series of candidates arose in this classification for which it is not yet know if they admit positive curvature. The connection of these candidates to the Hitchin self dual Einstein orbifolds is discussed as well, including the curvature properties of the Hitchin metrics.
Non-existence of cohomogeneity one Einstein metrics of two summands
6-dimensional nearly Kaehler manifolds of cohomogeneity one
On Ricci solitons of cohomogeneity one
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