Cartan connections and path structures with large automorphisms groups

Elisha Falbel (1, 2) , Martin Mion-Mouton (3) , Jose Miguel Veloso (4)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
3 IRMA - Institut de Recherche Mathématique Avancée
4 ICEN - Instituto de Ciências Exatas e Naturais

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.

Domaines: Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]

Elisha Falbel, Martin Mion-Mouton, Jose Miguel Veloso. Cartan connections and path structures with large automorphisms groups. International Journal of Mathematics, 2021, ⟨10.1142/S0129167X21400164⟩. ⟨hal-03214060v2⟩