The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry

2010/09/14 by Bernard Bonnard, Bonnard, Bernard, Grégoire Charlot +5
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1009.2612

arxiv created 2010/09/14 · arxiv updated 2010/09/15

Abstract

We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry. We compute estimations of the exponential map which allow us to describe the conjugate locus and the cut locus at a tangency point. We prove that this last one generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

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