2017/12/23 by Zoltán Muzsnay, Muzsnay, Zoltán
Mathematics · #53A60 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A60
paper · pdf · doi:10.48550/arxiv.1712.08806
arxiv created 2017/12/23 · arxiv updated 2017/12/27
There are two theories describing the linearizability of 3-webs: one is developed in the article "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp.2643-2654) and another in the article "On the Blaschke conjecture for 3-webs" (J. Geom. Anal. 16, 1 (2006), 69-115). Unfortunately, they cannot be both correct because on an explicit 3-web W they contradict: the first predicts that W is linearizable while the second states that W is not linearizable. The essential question beyond this particular 3-web is: which theory describes correctly the linearizability condition? In this paper we present a very short proof, due to J.-P.~Dufour, that W is linearizable, confirming the result of the first article.