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

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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Submitted on : Monday, September 13, 2010 - 6:03:37 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Tuesday, December 14, 2010 - 2:58:16 AM

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  • HAL Id : hal-00517193, version 1
  • ARXIV : 1009.2612

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Bernard Bonnard, Grégoire Charlot, Roberta Ghezzi, Gabriel Janin. The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry. 2010. ⟨hal-00517193⟩

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