Rank three geometry and positive curvature
Differential Geometry
2016-07-15 v1 Group Theory
Geometric Topology
Abstract
An axiomatic characterization of buildings of type due to Tits is used to prove that any cohomogeneity two polar action of type on a positively curved simply connected manifold is equivariantly diffeomorphic to a polar action on a rank one symmetric space. This includes two actions on the Cayley plane whose associated type geometry is not covered by a building.
Keywords
Cite
@article{arxiv.1607.04134,
title = {Rank three geometry and positive curvature},
author = {Fuquan Fang and Karsten Grove and Gudlaugur Thorbergsson},
journal= {arXiv preprint arXiv:1607.04134},
year = {2016}
}