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| HAL : hal-00410127, version 1 |
| arXiv : 0908.2564 |
| DOI : 10.1016/j.anihpc.2009.11.011 |
| Fiche détaillée |  Récupérer au format |
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| Annales de l'Institut Henri Poincare (C) Non Linear Analysis 27, 3 (2010) 793-307 |
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| Two-Dimensional Almost-Riemannian Structures with Tangency Points |
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| Andrei Agrachev 1Ugo Boscain 2 |
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| CORIDA Collaboration(s) |
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| (2010) |
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| Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points. |
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| 1 : | Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS) |
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Scuola Internazionale Superiore di Studi Avanzati/International School for Advanced Studies (SISSA/ISAS) |
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| 2 : | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| 3 : | Institut Fourier (IF) |
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CNRS : UMR5582 – Université Joseph Fourier - Grenoble I |
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| 4 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 5 : | CORIDA (INRIA Nancy - Grand Est / IECN / LMAM) |
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INRIA – CNRS : UMR7502 – Université de Lorraine |
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| Domaine | : | Mathématiques/Géométrie différentielle Mathématiques/Optimisation et contrôle |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00410127, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00410127 | |
| oai:hal.archives-ouvertes.fr:hal-00410127 | |
| Contributeur : Mario Sigalotti | |
| Soumis le : Lundi 17 Août 2009, 19:09:22 | |
| Dernière modification le : Vendredi 29 Avril 2011, 14:55:58 | |
