Geodesic
Asymptotic behaviour of the sphere and front of a flat sub-Riemannian structure on the Martinet distribution
Sbornik. Mathematics, Tome 213 (2022) no. 5, pp. 624-640 Cet article a éte moissonné depuis la source Math-Net.Ru

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The sphere and front of a flat sub-Riemannian structure on the Martinet distribution are surfaces with nonisolated singularities in three-dimensional space. The sphere is a subset of the front; it is not subanalytic at two antipodal points (the poles). The asymptotic behaviour of the sub-Riemannian sphere and Martinet front are calculated at these points: each surface is approximated by a pair of quasihomogeneous surfaces with distinct sets of weights in a neighbourhood of a pole. Bibliography: 13 titles.
Keywords: sphere of a sub-Riemannian structure, front of a sub-Riemannian structure, exponential map, Jacobi elliptic functions.
Mots-clés : Martinet distribution 
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I. A. Bogaevsky. Asymptotic behaviour of the sphere and front of a flat sub-Riemannian structure on the Martinet distribution. Sbornik. Mathematics, Tome 213 (2022) no. 5, pp. 624-640. http://geodesic.mathdoc.fr/item/SM_2022_213_5_a2/

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