On the geometry of cohomogeneity one manifolds with positive curvature

2007/07/23 by Wolfgang Ziller, Ziller, Wolfgang
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C20 #msc:53C25

paper · pdf · doi:10.48550/arxiv.0707.3345

25 pages

arxiv created 2007/07/23 · arxiv updated 2009/12/01

Abstract

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.

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