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Linearizable 3-webs and the Gronwall conjecture

Joseph Grifone·Zoltan Muzsnay·Jihad Saab
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Abstract

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.

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Joseph Grifone, Zoltan Muzsnay, Jihad Saab. 2006-02-23. Linearizable 3-webs and the Gronwall conjecture. https://arxiv.org/abs/math/0602535

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