On the role of abnormal minimizers in sub-Riemannian geometry

Bernard Bonnard; Emmanuel Trélat

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On the role of abnormal minimizers in sub-Riemannian geometry

Bernard Bonnard·Emmanuel Trélat

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Abstract

Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^\omega)$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.

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Bernard Bonnard, Emmanuel Trélat. 2006-07-18. On the role of abnormal minimizers in sub-Riemannian geometry. https://arxiv.org/abs/math/0607426

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