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The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry. (English) Zbl 1209.53014
Summary: 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.

53B20 Local Riemannian geometry
49K15 Optimality conditions for problems involving ordinary differential equations
53C17 Sub-Riemannian geometry
Full Text: DOI
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