Flat 3-webs of degree one on the projective plane
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 4, pp. 779-796.

Le but de ce travail est d’étudier les 3-tissus globaux ayant courbure nulle. En particular, nous nous intéressons aux feuilletages de degré 3 dont le tissu dual est plat. L’ingrédient principal est la transformée de Legendre, qui est un avatar de la dualité projective classique dans le domaine des équations différentielles. Nous obtenons une characterization des feuilletages de degré 3 sur le plan projectif dont les tissus duaux ont courbure nulle.

The aim of this work is to study global 3-webs with vanishing curvature. We wish to investigate degree 3 foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree 3 foliations whose Legendre transform are webs with zero curvature.

@article{AFST_2014_6_23_4_779_0,
     author = {Beltr\'an, A. and Falla Luza, M. and Mar{\'\i}n, D.},
     title = {Flat 3-webs of degree one on the projective plane},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {779--796},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
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     volume = {Ser. 6, 23},
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     year = {2014},
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Beltrán, A.; Falla Luza, M.; Marín, D. Flat 3-webs of degree one on the projective plane. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 4, pp. 779-796. doi : 10.5802/afst.1424. http://archive.numdam.org/articles/10.5802/afst.1424/

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