On the horoboundary and the geometry of rays of negatively curved manifolds

TL;DR

This paper explores the relationship between the horoboundary and the visual boundary of negatively curved Riemannian manifolds, providing explicit examples to illustrate phenomena that occur in non-simply connected cases.

Contribution

It offers a detailed comparison between horoboundary and visual boundary in negatively curved manifolds, especially highlighting differences in non-simply connected cases.

Findings

Identifies differences between horoboundary and visual boundary

Provides explicit examples of boundary phenomena

Analyzes effects of non-simply connected topology

Abstract

In this paper we try to compare the "horoboundary" of a (not necessarily simply connected) negatively curved complete Riemannian manifold X with the visual one and describe with explicit examples some phenomenoms wich may appear when X is not simply connected.