The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry
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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 phrasesAlmost-Riemannian geometry conjugate and cut loci sphere of small radius
2000 Mathematics Subject Classification53B20 49K15
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- 5.B. Bonnard and J.-B. Caillau, Singular metrics on the two-sphere in space mechanics. Preprint (2008), HAL, Vol. 00319299, pp. 1–25.Google Scholar
- 10.L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The mathematical theory of optimal processes. Interscience Publ. John Wiley and Sons, New York–London (1962).Google Scholar