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arXiv · 1712.08806

On the linearizability of 3-webs: end of controversy

Zoltán Muzsnay
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Abstract

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.

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Zoltán Muzsnay. 2017-12-23. On the linearizability of 3-webs: end of controversy. https://arxiv.org/abs/1712.08806

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