Communications in Analysis and Geometry

Volume 24 (2016)

Number 3

Rank three geometry and positive curvature

Pages: 487 – 520



Fuquan Fang (Department of Mathematics, Capital Normal University, Beijing, China)

Karsten Grove (Department of Mathematics, University of Notre Dame, Indiana, U.S.A.)

Gudlaugur Thorbergsson (Mathematisches Institut, Universität zu Köln, Germany)


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.

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article revised: 27 June 2016