Curvature exponent and geodesic dimension on Sard-regular Carnot groups
Abstract
In this paper we characterize the geodesic dimension NGEO and give a new lower bound to the curvature exponent NCE on Sard-regular Carnot groups. As an application, we give an example of step-two Carnot group on which NCE > NGEO: this answers a question posed by Rizzi in arXiv:1510.05960v4 [math.MG].
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