Ricci curvature in Carnot groups

Ludovic Rifford (1, 2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 McTAO - Mathematics for Control, Transport and Applications

We study metric contraction properties for metric spaces associated with left- invariant sub-Riemannian metrics on Carnot groups. We show that ideal sub- Riemannian structures on Carnot groups satisfy such properties and give a lower bound of possible curvature exponents in terms of the datas.

Domaines: Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]; Optimisation et contrôle [math.OC]

Ludovic Rifford. Ricci curvature in Carnot groups. Mathematical Control and Related Fields, 2013, 3 (4), pp.467. ⟨hal-00923326⟩