Abstract
We study the tangential case in two-dimensional almost-Riemannian geometry and analyze the connection with the Martinet case in sub-Riemannian geometry. We calculate estimates of the exponential map which allow us to describe the conjugate locus and the cut locus at a tangency point. We prove that this tangency point generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.
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G. Janin was supported by DGA/D4S/MRIS, under the supervision of J. Blanc-Talon, DGA/D4S/MRIS, Responsable de Domaine Ingénierie de l’Information. B. Bonnard and G. Charlot were supported by the ANR project GCM.
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Bonnard, B., Charlot, G., Ghezzi, R. et al. The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry. J Dyn Control Syst 17, 141–161 (2011). https://doi.org/10.1007/s10883-011-9113-4
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DOI: https://doi.org/10.1007/s10883-011-9113-4