Generic singularities of line fields on 2D manifolds

Ugo Boscain 1, 2, 3 Ludovic Sacchelli 2, 3 Mario Sigalotti 2, 3
2 GECO - Geometric Control Design
Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : Generic singularities of line fields have been studied for lines of principal curvature of embedded surfaces. In this paper we propose an approach to classify generic singularities of general line fields on 2D manifolds. The idea is to identify line fields as bisectors of pairs of vector fields on the manifold, with respect to a given conformal structure. The singularities correspond to the zeros of the vector fields and the genericity is considered with respect to a natural topology in the space of pairs of vector fields. Line fields at generic singularities turn out to be topologically equivalent to the Lemon, Star and Monstar singularities that one finds at umbilical points.
Type de document :
Article dans une revue
Differential Geometry and its Applications, Elsevier, 2016, Volume 49 (December 2016), pp.326-350
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01318515
Contributeur : Ludovic Sacchelli <>
Soumis le : jeudi 19 mai 2016 - 16:17:26
Dernière modification le : samedi 18 février 2017 - 01:13:55

Fichiers

LineFields.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01318515, version 1
  • ARXIV : 1605.06295

Citation

Ugo Boscain, Ludovic Sacchelli, Mario Sigalotti. Generic singularities of line fields on 2D manifolds. Differential Geometry and its Applications, Elsevier, 2016, Volume 49 (December 2016), pp.326-350. <hal-01318515>

Partager

Métriques

Consultations de
la notice

392

Téléchargements du document

84