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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Published inComptes rendus. Mathématique Vol. 361; no. G9; pp. 1491 - 1497
Main Authors Dufour, Jean-Paul, Lehmann, Daniel
Format Journal Article
LanguageEnglish
Published Académie des sciences 10.11.2023
Subjects
courbure
rang
tissus en courbes
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Summary: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.
ISSN:1778-3569
1778-3569
DOI:10.5802/crmath.500