Polynomial conserved quantities of Lie applicable surfaces

Francis Burstall, Udo Hertrich-Jeromin, Mason Pember, Wayne Rossman

Research output: Contribution to journalArticle

1 Citation (Scopus)
6 Downloads (Pure)

Abstract

Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quantities. These include isothermic and Guichard surfaces of conformal geometry and L-isothermic surfaces of Laguerre geometry. In this setting one can see that the well known transformations available for these surfaces are induced by the transformations of the underlying Lie applicable surfaces. We also consider linear Weingarten surfaces in this setting and develop a new Bäcklund-type transformation for these surfaces.
Original languageEnglish
Pages (from-to)505-546
Number of pages42
JournalManuscripta Mathematica
Volume158
Issue number3-4
Early online date26 Apr 2018
DOIs
Publication statusPublished - 31 Mar 2019

Fingerprint

Conserved Quantity
Polynomial
Weingarten Surface
Conformal Geometry
Gauge

Cite this

Polynomial conserved quantities of Lie applicable surfaces. / Burstall, Francis; Hertrich-Jeromin, Udo; Pember, Mason; Rossman, Wayne.

In: Manuscripta Mathematica, Vol. 158, No. 3-4, 31.03.2019, p. 505-546.

Research output: Contribution to journalArticle

Burstall, F, Hertrich-Jeromin, U, Pember, M & Rossman, W 2019, 'Polynomial conserved quantities of Lie applicable surfaces', Manuscripta Mathematica, vol. 158, no. 3-4, pp. 505-546. https://doi.org/10.1007/s00229-018-1033-0
Burstall, Francis ; Hertrich-Jeromin, Udo ; Pember, Mason ; Rossman, Wayne. / Polynomial conserved quantities of Lie applicable surfaces. In: Manuscripta Mathematica. 2019 ; Vol. 158, No. 3-4. pp. 505-546.
@article{55cd08b10df646929445c08e74e1f7f8,
title = "Polynomial conserved quantities of Lie applicable surfaces",
abstract = "Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quantities. These include isothermic and Guichard surfaces of conformal geometry and L-isothermic surfaces of Laguerre geometry. In this setting one can see that the well known transformations available for these surfaces are induced by the transformations of the underlying Lie applicable surfaces. We also consider linear Weingarten surfaces in this setting and develop a new B{\"a}cklund-type transformation for these surfaces.",
author = "Francis Burstall and Udo Hertrich-Jeromin and Mason Pember and Wayne Rossman",
year = "2019",
month = "3",
day = "31",
doi = "10.1007/s00229-018-1033-0",
language = "English",
volume = "158",
pages = "505--546",
journal = "Manuscripta Mathematica",
issn = "0025-2611",
publisher = "Springer New York",
number = "3-4",

}

TY - JOUR

T1 - Polynomial conserved quantities of Lie applicable surfaces

AU - Burstall, Francis

AU - Hertrich-Jeromin, Udo

AU - Pember, Mason

AU - Rossman, Wayne

PY - 2019/3/31

Y1 - 2019/3/31

N2 - Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quantities. These include isothermic and Guichard surfaces of conformal geometry and L-isothermic surfaces of Laguerre geometry. In this setting one can see that the well known transformations available for these surfaces are induced by the transformations of the underlying Lie applicable surfaces. We also consider linear Weingarten surfaces in this setting and develop a new Bäcklund-type transformation for these surfaces.

AB - Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quantities. These include isothermic and Guichard surfaces of conformal geometry and L-isothermic surfaces of Laguerre geometry. In this setting one can see that the well known transformations available for these surfaces are induced by the transformations of the underlying Lie applicable surfaces. We also consider linear Weingarten surfaces in this setting and develop a new Bäcklund-type transformation for these surfaces.

U2 - 10.1007/s00229-018-1033-0

DO - 10.1007/s00229-018-1033-0

M3 - Article

VL - 158

SP - 505

EP - 546

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 3-4

ER -