Rank three geometry and positive curvature

Fuquan Fang; Karsten Grove; Gudlaugur Thorbergsson

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arXiv · 1607.04134

Rank three geometry and positive curvature

Fuquan Fang·Karsten Grove·Gudlaugur Thorbergsson

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Abstract

An axiomatic characterization of buildings of type $\CC_3$ due to Tits is used to prove that any cohomogeneity two polar action of type $\CC_3$ 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 $\CC_3$ type geometry is not covered by a building.

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Fuquan Fang, Karsten Grove, Gudlaugur Thorbergsson. 2016-07-14. Rank three geometry and positive curvature. https://arxiv.org/abs/1607.04134

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