2018/11/08 by Mathieu Kohli, Kohli, Mathieu
Mathematics · Physics and Astronomy · Medicine · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1811.03429
In this paper we study the notion of geodesic curvature of smooth horizontal curves parametrized by arc lenght in the Heisenberg group, that is the simplest sub-Riemannian structure. Our goal is to give a metric interpretation of this notion of geodesic curvature as the first corrective term in the Taylor expansion of the distance between two close points of the curve.