2006/02/23 by Joseph Grifone, Grifone, Joseph, Zoltan Muzsnay +3
Mathematics · #53A60 #53C36 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A60 #msc:53C36
paper · pdf · doi:10.48550/arxiv.math/0602535
14 pages
arxiv created 2006/02/23 · arxiv updated 2009/12/01
In the article "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp.2643-2654), published in 2001, we studied the linearizability problem for 3-webs on a 2-dimensional manifold. Four years after the publication of our article, V.V.Goldberg and V.V.Lychagin in the paper "On linearization of planar three-webs and Blaschke's conjecture" (C.R.Acad. Sci. Paris, Ser. I. vol. 341. num 3 (2005)) obtained similar results by a different method and criticized our article by qualifying the proofs incomplete. However, they obtained false result on the linearizability of a certain web. We present here the complete version of our work with computations and explicit formulas, because we deem that their opinion concerning our work is unjustified.