94 research outputs found
On the geometry of cohomogeneity one manifolds with positive curvature
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.Comment: 25 page
Examples of Riemannian Manifolds with non-negative sectional curvature
An updated version with a few corrections.Comment: 32 page
Positively curved homogeneous metrics on spheres
We examine homogeneous metrics on spheres and determine which ones have
positive sectional curvature. The answer is subtle and surprisingly difficult
to prove. In some cases we also determine their pinching constants. This
completes the classification of all homogeneous metrics with positive curvature
(apart from one special Aloff Wallach space where the set of homogeneous
metrics is too large).Comment: 17 pages, 10 figure
- …