Tissus plats et feuilletages homogènes sur le plan projectif

2016/07/04 by Bedrouni, Samir, Marín, David
#14C21 #32S65 #53A60 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.00877

Abstract

The aim of this work is to study the foliations on the complex projective plane with flat Legendre transform (dual web). We establish some effective criteria for the flatness of the dual d-web of a homogeneous foliation of degree d and we describe some explicit examples. These results allow us to show that up to automorphism of ℙ² there are 11 homogeneous foliations of degree 3 with flat dual web. We will see also that it is possible, under certain assumptions, to bring the study of flatness of the dual web of a general foliation to the homogeneous framework. We get some classification results about foliations with non-degenerate singularities and flat Legendre transform.

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