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The wave front in sub-Riemannian geometry: The Martinet case. (Le front d’onde en géométrie sous-Riemannienne: Le cas Martinet.) (French) Zbl 0963.53016

Séminaire de théorie spectrale et géométrie. Année 1997-1998. St. Martin D’Hères: Université de Grenoble I, Institut Fourier, Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 16, 81-105 (1998).
Let \(F_1= (1+ \varepsilon y) { \partial \over {\partial x}}+ {{y^2}\over 2 } {\partial \over {\partial z}}\), \(F_2= {\partial\over {\partial y}}\) \((\varepsilon\in{\mathbb R})\) be the vector fields on a neighborhood of the origin in \({\mathbb R}^3\). The author considers a metric such that \(F_1\) and \(F_2\) are orthonormal, and the set \(W(0,r)\), the wave front, of points whose distance from the origin is \(r\) with respect to this metric. He gives a precise study on the intersection of the wave front with the plane \(\{y=0\}\), the Martinet plane.
For the entire collection see [Zbl 0904.00015].

MSC:

53C17 Sub-Riemannian geometry
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