Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions
type: Item
instance of: scholarly article
title: Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions
zbMATH Open document ID: 0973.53065
author: Frédéric Hélein
author: Pascal Romon
published in: Commentarii Mathematici Helvetici
publication date: 2001-11-16T00:00:00Z
review text: The authors obtain a Weierstrass-type formula for conformal Lagrangian immersions in Euclidean 4-space and show that the data satisfies a Dirac-type equation. They also propose an equivalent representation using quaternions, much simpler to handle in the case of Hamiltonian stationary Lagrangian immersions. As applications, they investigate immersed Klein bottles in the above family, classifying them and showing that they self-intersect.
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 49Q10
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 1562865
zbMATH Keywords: Weierstrass representation
zbMATH Keywords: Lagrangian surface
zbMATH Keywords: Hamiltonian stability
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
full work available at URL: s000140050144
OpenAlex ID: W2085544552
DOI: 10.1007/S000140050144
description: scientific article; zbMATH DE number 1562865