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

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 thi...

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Bibliographic Details
Published in:arXiv.org 2010-09
Main Authors: Bonnard, Bernard, Charlot, Grégoire, Ghezzi, Roberta, Janin, Gabriel
Format: Article
Language:English
Subjects:
Geometry
Loci
Two dimensional analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422