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arXiv · 1811.03429

A metric interpretation of the geodesic curvature in the Heisenberg group

Mathieu Kohli
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Abstract

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.

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Mathieu Kohli. 2018-11-08. A metric interpretation of the geodesic curvature in the Heisenberg group. https://arxiv.org/abs/1811.03429

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