Stable tangential family germs and singularities of their envelopes

Gianmarco Capitanio

doi:10.1016/j.crma.2005.09.014

Differential Geometry

Stable tangential family germs and singularities of their envelopes
[Germes stables de familles tangentielles et singularités de leurs enveloppes]

Présenté par : Vladimir Arnol'd

Gianmarco Capitanio ¹

¹ CEREMADE, université Paris-Dauphine, place du M. De Lattre De Tassigny, 75775 Paris cedex 16, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 8, pp. 503-508.

Résumé
Abstract

Une famille tangentielle est un système de courbes régulières, émanées tangentiellement par une autre courbe régulière. Nous classifions les germes de familles tangentielles qui sont stables par déformations parmi les familles tangentielles, et nous étudions les singularités des enveloppes correspondantes. Nous étudions aussi certaines applications de nos résultats en Géométrie Différentielle.

A tangential family is a system of regular curves emanating tangentially from another regular curve. We classify tangential family germs which are stable under deformations among tangential families and we study singularities of their envelopes. We also discuss some applications of our results to Differential Geometry.

Reçu le : 2005-06-22
Accepté le : 2005-09-07
Publié le : 2005-09-29

DOI : 10.1016/j.crma.2005.09.014

Affiliations des auteurs :

Gianmarco Capitanio ¹

¹ CEREMADE, université Paris-Dauphine, place du M. De Lattre De Tassigny, 75775 Paris cedex 16, France

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     title = {Stable tangential family germs and singularities of their envelopes},
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Gianmarco Capitanio. Stable tangential family germs and singularities of their envelopes. Comptes Rendus. Mathématique, Volume 341 (2005) no. 8, pp. 503-508. doi : 10.1016/j.crma.2005.09.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.014/

Bibliographie
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