Journal of Dynamical and Control Systems

, Volume 17, Issue 1, pp 141–161 | Cite as

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

  • B. BonnardEmail author
  • G. Charlot
  • R. Ghezzi
  • G. Janin


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.

Key words and phrases

Almost-Riemannian geometry conjugate and cut loci sphere of small radius 

2000 Mathematics Subject Classification

53B20 49K15 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneDijon CedexFrance
  2. 2.Institut FourierSt Martin d’HéresFrance France
  3. 3.SISSA/ISASTriesteItaly

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