Ricci curvatures in Carnot groups
Copyright policy )Ricci curvatures in Carnot groups
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.
29 pages, 1 figure
Mathematics - Differential Geometry, Mathematics - Metric Geometry, Differential Geometry (math.DG), Optimization and Control (math.OC), FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Metric Geometry (math.MG), [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], Mathematics - Optimization and Control
Mathematics - Differential Geometry, Mathematics - Metric Geometry, Differential Geometry (math.DG), Optimization and Control (math.OC), FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Metric Geometry (math.MG), [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], Mathematics - Optimization and Control
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