Ricci curvatures in Carnot groups

TL;DR

This paper investigates Ricci curvature properties in Carnot groups with sub-Riemannian metrics, establishing contraction properties for ideal structures and providing bounds on curvature exponents based on group data.

Contribution

It introduces contraction properties for sub-Riemannian structures on Carnot groups and derives lower bounds for curvature exponents from the group's data.

Findings

Ideal sub-Riemannian structures satisfy metric contraction properties

Lower bounds for curvature exponents are established

Results apply to a broad class of Carnot groups

Abstract

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.