On the role of abnormal minimizers in sub-riemannian geometry | Zendy

Bernard Bonnard | Zendy; Emmanuel Trélat | Zendy

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On the role of abnormal minimizers in sub-riemannian geometry

Author(s) -

Bernard Bonnard,

Emmanuel Trélat

Publication year - 2001

Publication title -

annales de la faculté des sciences de toulouse mathématiques

Language(s) - English

Resource type - Journals

eISSN - 2258-7519

pISSN - 0240-2963

DOI - 10.5802/afst.998

Subject(s) - riemannian geometry , geometry , metric (unit) , rank (graph theory) , mathematics , fundamental theorem of riemannian geometry , omega , distribution (mathematics) , combinatorics , physics , mathematical analysis , scalar curvature , engineering , operations management , curvature , quantum mechanics

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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