Injectivity Radius and Cartan Polyhedron for Simply Connected Symmetric Spaces*

Abstract

The author explores the relationship between the cut locus of an arbitrary simply connected and compact Riemannian symmetric space and the Cartan polyhedron of corresponding restricted root system, and computes the injectivity radius and diameter for every type of irreducible ones.

Keywords

Cartan polyhedron / Restricted root system / Orthogonal involutive Lie algebra / Dynkin diagram / Stake diagram / 53C35

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