2019/06/27 by J. P. Dufour, Jean Paul Dufour, Dufour, Jean Paul
Computer Science · Mathematics · #53A60 #Algorithms and Data Compression #Differential Geometry (math.DG) #FOS: Mathematics #Mobile Agent-Based Network Management #math.DG #msc:53A60
paper · pdf · doi:10.48550/arxiv.1906.11545
12 pages
arxiv created 2019/06/27 · openalex publication_date 2019/06/27 · arxiv updated 2019/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we will explore a way to prove the hundred years old Gronwall's conjecture: if two plane linear 3-webs with non-zero curvature are locally isomorphic, then the isomorphism is a homography. Using recent results of S. I. Agafonov, we exhibit an invariant, the \sl characteristic, attached to each generic point of such a web, with the following property: if a diffeomorphism interchanges two such linear webs, sending a point of the first to a point of the second which have the same characteristic, then this diffeomomorphism is locally a homography.