Contents Online

# Communications in Analysis and Geometry

## Volume 24 (2016)

### Number 3

### Rank three geometry and positive curvature

Pages: 487 – 520

DOI: http://dx.doi.org/10.4310/CAG.2016.v24.n3.a3

#### Authors

#### Abstract

An axiomatic characterization of buildings of type $\mathsf{C}_3$ due to Tits is used to prove that any cohomogeneity two polar action of type $\mathsf{C}_3$ 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 $\mathsf{C}_3$ type geometry is not covered by a building.

article revised: 27 June 2016