Veronese webs and transversally Veronese foliations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1017.53017
author: Marie-H'el`ene Rigal
publication date: 2002-04-11T00:00:00Z
Mathematics Subject Classification ID: 53A60
zbMATH DE Number: 1727399
zbMATH Keywords: foliations
zbMATH Keywords: flows
zbMATH Keywords: bi-Hamiltonian systems
zbMATH Keywords: conformally parallelizable structure
zbMATH Keywords: rigidity
MaRDI profile type: Publication
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title: Veronese webs and transversally Veronese foliations
review text: A web on a surface \(S\) consists of three codimension-one foliations, which are transversal to each other everywhere on \(S\). A foliated web on a 3-manifold \(M\) is a flow consisting of the intersection of three codimension-one foliations, which are transversal to each other everywhere on \(M\). Now, a conformally parallelizable (CP) structure on an \(n\)-dimensional manifold \(M\) corresponds to \(n+1\) foliations of dimension 1, whose associated directions are mutually transversal, and span the entire tangent space \(T_XM\) at every point \(X\in M\). In this paper some elementary facts concerning these structures and their rigidity are studied and the foliations possessing a transversally CP structure are considered. Finally classifications of the transversally CP flows and applications to bi-Hamiltonian systems in odd dimension are given.NEWLINENEWLINEFor the entire collection see [Zbl 0983.00024].
reviewed by: Stylianos Stamatakis
description: scientific article; zbMATH DE number 1727399