Joseph Grifone, Zoltan Muzsnay, Jihad Saab
Published 2006-02-23Version 1
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.
On the problem of linearizability of a 3-web
On the Blaschke conjecture for 3-webs
Gronwall's conjecture for 3-webs with infinitesimal symmetries
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