Local reflexion spaces

TL;DR

This paper introduces local reflexion spaces as a generalization of symmetric spaces and explores their characterization via locally flat Cartan connections.

Contribution

It extends the concept of symmetric spaces to local reflexion spaces and establishes conditions under which they correspond to specific Cartan connections.

Findings

Local reflexion spaces generalize symmetric spaces.

Characterization of local reflexion spaces via flat Cartan connections.

Conditions for equivalence between local reflexion spaces and Cartan geometries.

Abstract

A reflexion space is generalization of a symmetric space introduced by O. Loos. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local reflexion spaces are equivalently given by a locally flat Cartan connection of certain type.