The Ribaucour transformation for flat Lagrangian submanifolds.
type: Item
instance of: scholarly article
title: The Ribaucour transformation for flat Lagrangian submanifolds.
zbMATH Open document ID: 1036.53038
DOI: 10.1007/BF02921825
author: Marcos Dajczer
author: Ruy Tojeiro
published in: The Journal of Geometric Analysis
publication date: 2000-12-11T00:00:00Z
review text: The authors study Ribaucour transformations for flat Lagrangian submanifolds of (flat) complex \(n\)-space and complex projective space. They show that such submanifolds of complex \(n\)-space are in correspondence with the solutions of a completely integrable system of PDEs which describe a system of globally defined principal coordinates on the submanifold: this system is apparently one of the type which Darboux named an ``E-system''. The Ribaucour transformations generate new submanifolds from old. The corresponding theory for submanifolds of \(\mathbb{C} \text{P}^n\) makes use of the fact that flat Lagrangian submanifolds of \(\mathbb{C} \text{P}^n\) are precisely the images, under Hopf fibration, of flat Lagrangian submanifolds of complex \(n+1\)-space which also lie in \(S^{2n+1}\).
reviewed by: Ian McIntosh
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 37K35
zbMATH DE Number: 1542078
zbMATH Keywords: complex \(n\)-space
zbMATH Keywords: completely integrable system
zbMATH Keywords: globally defined principal coordinates
zbMATH Keywords: Hopf fibration
MaRDI profile type: Publication
cites work: Q4173915
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Wikidata QID: Q125883680
description: scientific article; zbMATH DE number 1542078