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

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

2010-09-14

arxiv.org/abs/1009.2612v1

Mathematics

Optimization and Control

Scientific paper

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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