2006/02/23 by Zoltán Muzsnay, Zoltan Muzsnay, Muzsnay, Zoltan
Engineering · Mathematics · #53A60 #53C36 #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #Mathematics and Applications #Structural Analysis and Optimization #math.DG #msc:53A60 #msc:53C36
paper · pdf · doi:10.48550/arxiv.math/0602536
9 pages
arxiv created 2006/02/23 · openalex publication_date 2006/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the linearizability problem for 3-webs on a 2-dimensional manifold. With an explicit computation based on the theory developed in the paper "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp. 2643-2654), we examine a 3-web whose linearizability was claimed in the same paper. We show that, contrary to the statement of the papers "On the Blaschke conjecture for 3-webs" (arXiv: math.DG/0411460) and "On linearization of planar three-webs and Blaschke's conjecture", (C.R.Acad. Sci. Paris, Ser. I. vol. 341. num 3 (2005)), this particular web is linearizable. We compute explicitly the affine deformation tensor and the corresponding flat linear connection adapted to the web which linearizes it.