The geometry of hyperbolic lines in polar spaces

TL;DR

This paper explores the geometric properties of hyperbolic lines within polar spaces, providing characterizations and demonstrating applications across group theory, Lie algebras, and graph theory.

Contribution

It introduces new geometric characterizations of hyperbolic lines in polar spaces and connects these structures to various mathematical fields.

Findings

Characterizations of hyperbolic lines in polar spaces

Applications in group theory and Lie algebras

Connections to graph theory

Abstract

In this paper we consider partial linear spaces induced on the point set of a polar space, but with as lines the hyperbolic lines of this polar space. We give some geometric characterizations of these and related spaces. The results have applications in group theory, in the theory of Lie algebras and in graph theory.