On the linearizability of 3-webs: End of controversy

Zoltán Muzsnay

doi:10.1016/j.crma.2017.12.006

Differential geometry

On the linearizability of 3-webs: End of controversy

Presented by: the Editorial Board

Zoltán Muzsnay ¹

¹ Institute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, Hungary

Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 97-99.

Abstract
Résumé

There are two theories describing the linearizability of 3-webs: one is developed in [10] and another in [8]. Unfortunately they cannot be both correct because on an explicit 3-web $W_{0}$ they contradict: the first predicts that $W_{0}$ is linearizable, while the second states that $W_{0}$ 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 $W_{0}$ is linearizable, confirming the result of [10].

Il existe deux théories décrivant la linéarisabilité des 3-tissus : l'une est développée dans [10], l'autre dans [8]. Malheureusement, elles ne peuvent pas être correctes toutes les deux, car sur un 3-tissu $W_{0}$ elles se contredisent : la première prédit que le tissu $W_{0}$ est linéarisable, tandis que la seconde affirme que $W_{0}$ n'est pas linéarisable. La question essentielle au-delà de ce 3-tissu particulier est : quelle théorie décrit correctement la condition de linéarisabilité ? Dans cet article, nous présentons une preuve très courte, due à J.-P. Dufour, de ce que le tissu $W_{0}$ est linéarisable, confirmant le résultat de [10].

Received: 2017-01-03
Accepted: 2017-12-14
Published online: 2017-12-23

DOI: 10.1016/j.crma.2017.12.006

Author's affiliations:

Zoltán Muzsnay ¹

¹ Institute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, Hungary

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Zoltán Muzsnay. On the linearizability of 3-webs: End of controversy. Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 97-99. doi : 10.1016/j.crma.2017.12.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.12.006/

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Cited by Sources:

^☆ This work is partially supported by the EFOP-3.6.2-16-2017-00015 project and by the EFOP-3.6.1-16-2016-00022 project. The projects have been supported by the European Union, co-financed by the European Social Fund.

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