Surfaces on Lie groups, on Lie algebras, and their integrability (with an appendix by Juan Carlos Alvarez Paiva)
type: Item
instance of: scholarly article
title: Surfaces on Lie groups, on Lie algebras, and their integrability (with an appendix by Juan Carlos Alvarez Paiva)
zbMATH Open document ID: 0864.53003
DOI: 10.1007/BF02102436
published in: Communications in Mathematical Physics
publication date: 1996-08-22T00:00:00Z
review text: The method of the immersion of a 2-dimensional surface into a 3-dimensional Euclidean space is used to study surfaces in Lie groups and surfaces in Lie algebras. The \(n\)-dimensional generalization is also given. It is shown that a particular case of the general theory yields the characterization of an arbitrary surface in terms of \(2\times 2\) matrices. The use of Lie point groups provides an effective method for both finding as well as classifying integrable surfaces. It is proven that the integrable case of inverse harmonic \(H\) is the only case for which the Gauss-Codazzi equations admit a nontrivial Lie point group of transformations. In an appendix written by J. C. Alvarez it is shown the connection of the results obtained by the authors with Cartan's method of moving frames.
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 906570
zbMATH Keywords: immersion
zbMATH Keywords: Lie point groups
zbMATH Keywords: integrable surfaces
zbMATH Keywords: Gauss-Codazzi equations
author: A. S. Fokas
author: I. M. Gel'fand
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
Wikidata QID: Q115392793
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full work available at URL: https://doi.org/10.1007/bf02102436
OpenAlex ID: W1999269083
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description: scientific article; zbMATH DE number 906570