Rigidity of ideal symmetric sets

TL;DR

This paper characterizes higher rank model geometries such as symmetric spaces and Euclidean buildings among Hadamard spaces using properties of antipodal sets at infinity.

Contribution

It introduces a new characterization method for higher rank geometries based on antipodal sets at infinity, advancing the understanding of Hadamard spaces.

Findings

Higher rank geometries are characterized by antipodal sets at infinity.

The approach distinguishes symmetric spaces and Euclidean buildings from other Hadamard spaces.

The results provide a new tool for classifying non-positively curved spaces.

Abstract

We characterize higher rank model geometries -- Riemannian symmetric spaces, Euclidean buildings and products -- among Hadamard spaces by using antipodal sets at infinity.