Tits geometry on ideal boundaries of Busemann non-positively curved space

TL;DR

This paper introduces a new framework for analyzing the ideal boundaries of Busemann spaces by generalizing Tits metric comparisons, enabling the application of CAT(0) space properties without relying on the metric.

Contribution

It develops a collection of binary relations on ideal boundaries of Busemann spaces, extending Tits metric comparison techniques beyond CAT(0) spaces.

Findings

Established relations generalizing Tits metric comparisons

Enabled analysis of Busemann spaces using CAT(0) properties

Provided new tools for geometric analysis of non-positively curved spaces

Abstract

Let $X$ be a non-compact proper Busemann space. We introduce a collection of binary relations on its ideal boundaries generalizing comparison of Tits metric with two key values $\pi$ and $\pi/2$. This allows to use properties of Tits metric known for CAT(0)-space without metric itself.