Incidence axioms for the boundary at infinity of complex hyperbolic spaces

TL;DR

This paper characterizes the boundary at infinity of complex hyperbolic spaces using four incidence axioms, providing a geometric framework for understanding their boundary structure.

Contribution

It introduces a new axiomatic characterization of the boundary at infinity of complex hyperbolic spaces as a Ptolemy space satisfying specific incidence conditions.

Findings

Boundary at infinity characterized by four incidence axioms

Boundary space shown to be a compact Ptolemy space

Provides a geometric framework for complex hyperbolic boundaries

Abstract

We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.