Ricci curvatures in Carnot groups

2013/05/26 by Ludovic Rifford, Rifford, Ludovic · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC) #math.DG #math.MG #math.OC

paper · pdf · doi:10.48550/arxiv.1305.6057

29 pages, 1 figure

arxiv created 2013/05/26 · arxiv updated 2013/05/28

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.

Cited by

• Universal non-CD of sub-Riemannian manifolds
• On the lower bound of the curvature exponent on step-two Carnot groups

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