Cartan connections and path structures with large automorphisms groups

TL;DR

This paper classifies three-dimensional compact manifolds with strict path structures and large automorphism groups, demonstrating that their associated Cartan connections have constant curvature, thus revealing their geometric structure.

Contribution

It provides a classification of such manifolds using Cartan connections with constant curvature, under the condition of non-compact automorphism groups.

Findings

Automorphism group is non-compact for classified manifolds

Associated Cartan connection has constant curvature

Classification applies to three-dimensional compact manifolds

Abstract

We classify compact manifolds of dimension three equipped with a path structure and a fixed contact form (which we refer to as a strict path structure) under the hypothesis that their automorphism group is non-compact. We use a Cartan connection associated to the structure and show that its curvature is constant.