
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.
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