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

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