Cartan connections and path structures with large automorphisms groups

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.

International Journal of Mathematics, 2021. In this (unpublished) improved version, we withdraw the hypothesis of a dense orbit of the automorphism group in the main Theorem 1.1 when the structure is class C^3