Flat 3-webs of degree one on the projective plane
A. Beltrán; M. Falla Luza; D. Marín
Annales de la faculté des sciences de Toulouse Mathématiques (2014)
- Volume: 23, Issue: 4, page 779-796
- ISSN: 0240-2963
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topBeltrán, A., Falla Luza, M., and Marín, D.. "Flat 3-webs of degree one on the projective plane." Annales de la faculté des sciences de Toulouse Mathématiques 23.4 (2014): 779-796. <http://eudml.org/doc/275404>.
@article{Beltrán2014,
abstract = {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.},
author = {Beltrán, A., Falla Luza, M., Marín, D.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
number = {4},
pages = {779-796},
publisher = {Université Paul Sabatier, Toulouse},
title = {Flat 3-webs of degree one on the projective plane},
url = {http://eudml.org/doc/275404},
volume = {23},
year = {2014},
}
TY - JOUR
AU - Beltrán, A.
AU - Falla Luza, M.
AU - Marín, D.
TI - Flat 3-webs of degree one on the projective plane
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 4
SP - 779
EP - 796
AB - 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.
LA - eng
UR - http://eudml.org/doc/275404
ER -
References
top- Brunella (M.).— Birational geometry of foliations. IMPA (2000). Zbl1082.32022MR1948251
- Fischer (G.).— Plane Algebraic Curves, volume 15 of Student Mathematical Library. American Mathematical Society (2001). Zbl0971.14026MR1836037
- Hénaut (A.).— Planar web geometry through abelian relations and singularities. Nankai Tracts Math., 11, p. 269-295 (2006). Zbl1133.53012MR2313337
- Ince (E.).— Ordinary Differential Equations. Dover Publications (1944). Zbl0063.02971MR10757
- Marín (D.), Pereira (J.V.).— Rigid at webs on the projective plane. Asian Journal of Mathematics, 17p. 163-192 (2013). Zbl1330.53020
- Pereira (J. V.).— Vector fields, invariant varieties and linear systems. Ann. Inst. Fourier (Grenoble), 51(5)p. 1385-1405 (2001). Zbl1107.37038MR1860669
- Pereira (J. V.), Pirio (L.).— Classification of exceptional CDQL webs on compact complex surfaces. IMRN, 12p. 2169-2282 (2010). Zbl1208.53011MR2652221
- Pereira (J. V.), Pirio (L.).— An invitation to web geometry. IMPA (2009). Zbl1184.53002MR2536234
- Ripoll (O.).— Géométrie des tissus du plan et équations differentielles. Thèse de Doctorat de l’Université Bordeaux 1 (2005).
- Ripoll (O.).— Properties of the connection associated with planar webs and applications. Preprint arXiv:math/0702321v2, (2007).
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