Lie geometry of linear Weingarten surfaces

Francis E. Burstall; Udo Hertrich-Jeromin; Wayne Rossman

doi:10.1016/j.crma.2012.03.018

Differential Geometry

Lie geometry of linear Weingarten surfaces
[La géométrie de Lie des surfaces de Weingarten linéaires]

Présenté par : Jean-Pierre Demailly

Francis E. Burstall ¹ ; Udo Hertrich-Jeromin ¹ ; Wayne Rossman ²

¹ Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
² Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 413-416.

Résumé
Abstract

Nous montrons que les surfaces de Weingarten linéaires peuvent être présentées comme des surfaces Ω spéciales. Ensuite, nous discutons une caractérisation des surfaces de Weingarten linéaires de type Bryant.

We show how linear Weingarten surfaces appear as special Ω-surfaces and give a characterization of those linear Weingarten surfaces that allow a Weierstrass type representation.

Reçu le : 2011-01-18
Accepté le : 2012-03-23
Publié le : 2012-03-30

DOI : 10.1016/j.crma.2012.03.018

Affiliations des auteurs :

Francis E. Burstall ¹ ; Udo Hertrich-Jeromin ¹ ; Wayne Rossman ²

¹ Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
² Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

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     title = {Lie geometry of linear {Weingarten} surfaces},
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     doi = {10.1016/j.crma.2012.03.018},
     language = {en},
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Francis E. Burstall; Udo Hertrich-Jeromin; Wayne Rossman. Lie geometry of linear Weingarten surfaces. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 413-416. doi : 10.1016/j.crma.2012.03.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.03.018/

Bibliographie
Cité par

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Udo Hertrich-Jeromin; Mason Pember; Denis Polly Channel linear Weingarten surfaces in space forms, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Volume 64 (2023) no. 4, p. 969 | DOI:10.1007/s13366-022-00664-w
Mason Pember Weierstrass-type representations, Geometriae Dedicata, Volume 204 (2020) no. 1, p. 299 | DOI:10.1007/s10711-019-00456-y
Francis E. Burstall; Udo Hertrich-Jeromin; Mason Pember; Wayne Rossman Polynomial conserved quantities of Lie applicable surfaces, manuscripta mathematica, Volume 158 (2019) no. 3-4, p. 505 | DOI:10.1007/s00229-018-1033-0
Mason Pember; Gudrun Szewieczek Channel surfaces in Lie sphere geometry, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Volume 59 (2018) no. 4, p. 779 | DOI:10.1007/s13366-018-0394-6
Wai Yeung Lam; Ulrich Pinkall Isothermic triangulated surfaces, Mathematische Annalen, Volume 368 (2017) no. 1-2, p. 165 | DOI:10.1007/s00208-016-1424-z
Claudiano Goulart; Keti Tenenblat On Bäcklund and Ribaucour transformations for surfaces with constant negative curvature, Geometriae Dedicata, Volume 181 (2016) no. 1, p. 83 | DOI:10.1007/s10711-015-0113-5

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