2022/11/09 by Dufour Jean-Paul, Daniel Lehmann, Jean-Paul, Dufour +1
Arts and Humanities · Mathematics · #53A60 #American Literature and Culture #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2211.05188
openalex publication_date 2022/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, up to isomorphism, and give examples of invariants of these classes allowing in particular to distinguish the so-called quadrilateral webs among them.