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arXiv · 1505.00129

Courbure des tissus planaires d\'efinis implicitement par une \'equation diff\'erentielle polynomiale en y'. Programmation

Jean-Paul Dufour·Daniel Lehmann
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Abstract

The aim of this paper is mainly, after some theoretical explanations, to provide a program on Maple for computing, whatever be d, the curvature of the planar d-web implicitely defined by a differential equation F(x,y,y')=0, F being polynomial of degree d with respect to y'. Moreover, we prove in the appendix a "concentration theorem" for any calibrated ordinary $d$-web of codimension one in n-dimensional manifold (in particular for any planar web). Its curvature matrix, relatively to an "adapted" trivialization, is concentrated on the (n-2+k0)!/(n-2)!k0! last lines (the last line if n=2), k0 denoting the integer such that d=(n-1+k0)!/(n-1)!(k0)!$.

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Jean-Paul Dufour, Daniel Lehmann. 2015-05-01. Courbure des tissus planaires d\'efinis implicitement par une \'equation diff\'erentielle polynomiale en y'. Programmation. https://arxiv.org/abs/1505.00129

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