Geometry on real projective Cayley-Klein spaces

TL;DR

This paper explores the geometry of real Cayley-Klein spaces, focusing on defining a practical distance function between anisotropic subspaces to simplify calculations and reduce case distinctions.

Contribution

It introduces a new approach to defining a distance function on real Cayley-Klein spaces that facilitates easier computation between anisotropic subspaces.

Findings

A novel distance function for real Cayley-Klein spaces

Simplified calculations for distances between anisotropic subspaces

Reduced case distinctions in geometric computations

Abstract

We investigate several topics of the geometry on real Cayley-Klein spaces. An important concern for us is to define a distance function on the projective space in such a way that the distance between two anisotropic subspaces of the same dimension can be easily calculated and case distinctions are avoided as far as possible.