Étude des $(n+1)$-tissus de courbes en dimension $n$
For $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we first define a generalization of the well known Blaschke curvature of the dimension two, which vanishes iff the web has the maximum possible rank which is one. But, contrary to the dimension two where all 3-webs of rank one are lo...
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.500/ |
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| author | Dufour, Jean-Paul Lehmann, Daniel |
| author_facet | Dufour, Jean-Paul Lehmann, Daniel |
| author_sort | Dufour, Jean-Paul |
| collection | DOAJ |
| description | For $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we first define a generalization of the well known Blaschke curvature of the dimension two, which vanishes iff the web has the maximum possible rank which is one. But, contrary to the dimension two where all 3-webs of rank one are locally isomorphic, we prove that there are infinitely many classes of isomorphism for germs of 4-webs by curves of rank one in the dimension three: we provide a procedure for building all of them, and give examples of invariants of these classes allowing in particular to distinguish the so-called quadrilateral webs among them. |
| format | Article |
| id | doaj-art-977b038a138d4080950db63aa492c03c |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-977b038a138d4080950db63aa492c03c2025-02-07T11:10:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91491149710.5802/crmath.50010.5802/crmath.500Étude des $(n+1)$-tissus de courbes en dimension $n$Dufour, Jean-Paul0Lehmann, Daniel11 rue du Portalet 34820 Teyran, France; ancien professeur à l’Université de Montpellier II4 rue Becagrun 30980 Saint Dionisy, France; ancien professeur à l’Université de Montpellier IIFor $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we first define a generalization of the well known Blaschke curvature of the dimension two, which vanishes iff the web has the maximum possible rank which is one. But, contrary to the dimension two where all 3-webs of rank one are locally isomorphic, we prove that there are infinitely many classes of isomorphism for germs of 4-webs by curves of rank one in the dimension three: we provide a procedure for building all of them, and give examples of invariants of these classes allowing in particular to distinguish the so-called quadrilateral webs among them.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.500/tissus en courbescourburerang |
| spellingShingle | Dufour, Jean-Paul Lehmann, Daniel Étude des $(n+1)$-tissus de courbes en dimension $n$ Comptes Rendus. Mathématique tissus en courbes courbure rang |
| title | Étude des $(n+1)$-tissus de courbes en dimension $n$ |
| title_full | Étude des $(n+1)$-tissus de courbes en dimension $n$ |
| title_fullStr | Étude des $(n+1)$-tissus de courbes en dimension $n$ |
| title_full_unstemmed | Étude des $(n+1)$-tissus de courbes en dimension $n$ |
| title_short | Étude des $(n+1)$-tissus de courbes en dimension $n$ |
| title_sort | etude des n 1 tissus de courbes en dimension n |
| topic | tissus en courbes courbure rang |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.500/ |
| work_keys_str_mv | AT dufourjeanpaul etudedesn1tissusdecourbesendimensionn AT lehmanndaniel etudedesn1tissusdecourbesendimensionn |