On planar web geometry through Abelian relations and connections
type: Item
instance of: scholarly article
title: On planar web geometry through Abelian relations and connections
zbMATH Open document ID: 1069.53020
author: Alain Hénaut
published in: Annals of Mathematics. Second Series
publication date: 2004-12-29T00:00:00Z
review text: Using a canonical normalization of a planar \(d\)-web given by a differential equation \(F(x,y,y')=0\) the author gives a method to find analytical invariants of this \(d\)-web. A connection \((\varepsilon, \bigtriangledown)\) associated with a planar \(d\)-web is constructed. The connection is a generalization of the Blaschke 3-web connection and its \(\mathbb{C}\)-vector space of horizontal sections is isomorphic to the \(\mathbb{C}\)-vector space of Abelian relations of \(d\)-webs. The connection \((\varepsilon, \bigtriangledown)\) is integrable if and only if \(d\)-web is of maximal rank. Using only the methods introduced in his paper the author proves the main theorem for linear \(d\)-webs.
Mathematics Subject Classification ID: 53A60
zbMATH DE Number: 2123900
zbMATH Keywords: \(d\)-web
zbMATH Keywords: linear web
zbMATH Keywords: Abelian relation of web
zbMATH Keywords: rank of web
zbMATH Keywords: connection of web
reviewed by: A. M. Shelekhov
MaRDI profile type: Publication
full work available at URL: annals.2004.159.425
OpenAlex ID: W2063114936
DOI: 10.4007/ANNALS.2004.159.425
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description: scientific article; zbMATH DE number 2123900