Comptes Rendus
no. 11-12
Differential Geometry
Lie geometry of flat fronts in hyperbolic space
[La géométrie de Lie des fronts plats dans l'éspace hyperbolique]

Présenté par : Marcel Berger

Francis E. Burstall1 ; Udo Hertrich-Jeromin1 ; Wayne Rossman2
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 348 (2010) no. 11-12, pp. 661-664.

Nous proposons un point de vue de Lie géometrie sur les fronts plats dans l'éspace hyperbolique comme des surfaces Ω spéciales. Nous discutons ensuite la déformation Lie géometrique des fronts plats.

We propose a Lie geometric point of view on flat fronts in hyperbolic space as special Ω-surfaces and discuss the Lie geometric deformation of flat fronts.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.04.018

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 
@article{CRMATH_2010__348_11-12_661_0,
     author = {Francis E. Burstall and Udo Hertrich-Jeromin and Wayne Rossman},
     title = {Lie geometry of flat fronts in hyperbolic space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {661--664},
     publisher = {Elsevier},
     volume = {348},
     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.018},
     language = {en},
}
TY  - JOUR
AU  - Francis E. Burstall
AU  - Udo Hertrich-Jeromin
AU  - Wayne Rossman
TI  - Lie geometry of flat fronts in hyperbolic space
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 661
EP  - 664
VL  - 348
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crma.2010.04.018
LA  - en
ID  - CRMATH_2010__348_11-12_661_0
ER  - 
%0 Journal Article
%A Francis E. Burstall
%A Udo Hertrich-Jeromin
%A Wayne Rossman
%T Lie geometry of flat fronts in hyperbolic space
%J Comptes Rendus. Mathématique
%D 2010
%P 661-664
%V 348
%N 11-12
%I Elsevier
%R 10.1016/j.crma.2010.04.018
%G en
%F CRMATH_2010__348_11-12_661_0
Francis E. Burstall; Udo Hertrich-Jeromin; Wayne Rossman. Lie geometry of flat fronts in hyperbolic space. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 661-664. doi : 10.1016/j.crma.2010.04.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.018/

[1] W. Blaschke Vorlesungen über Differentialgeometrie III, Grundlehren, vol. XXIX, Springer, Berlin, 1929

[2] A. Demoulin Sur les surfaces R et les surfaces Ω, Comptes Rendus, Volume 153 (1911), pp. 590-593 (705–707)

[3] A. Demoulin Sur les surfaces Ω, Comptes Rendus, Volume 153 (1911), pp. 927-929

[4] J. Gálvez; A. Martínez; F. Milán Flat surfaces in the hyperbolic 3-space, Math. Ann., Volume 316 (2000), pp. 419-435

[5] U. Hertrich-Jeromin Introduction to Möbius Differential Geometry, Cambridge Univ. Press, Cambridge, 2003

[6] T. Hoffmann; W. Rossman; T. Sasaki; M. Yoshida Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3-space, 2009 (Eprint) | arXiv

[7] M. Kokubu; W. Rossman; K. Saji; M. Umehara; K. Yamada Singularities of flat fronts in hyperbolic space, Pacific J. Math., Volume 221 (2005), pp. 303-352

[8] M. Kokubu; W. Rossman; M. Umehara; K. Yamada Flat fronts in hyperbolic space and their caustics, J. Math. Soc. Japan, Volume 59 (2007), pp. 265-299

[9] E. Musso; L. Nicolodi Deformation and applicability of surfaces in Lie sphere geometry, Tôhoku Math. J., Volume 58 (2006), pp. 161-187

  • Udo Hertrich-Jeromin; Mason Pember; Denis Polly Channel linear Weingarten surfaces in space forms, Beiträge zur Algebra und Geometrie, Volume 64 (2023) no. 4, pp. 969-1009 | DOI:10.1007/s13366-022-00664-w | Zbl:1527.53003
  • Joseph Cho; Mason Pember; Gudrun Szewieczek Constrained elastic curves and surfaces with spherical curvature lines, Indiana University Mathematics Journal, Volume 72 (2023) no. 5, pp. 2059-2099 | DOI:10.1512/iumj.2023.72.9487 | Zbl:1544.53013
  • Udo Hertrich-Jeromin; Gudrun Szewieczek Discrete cyclic systems and circle congruences, Annali di Matematica Pura ed Applicata. Serie Quarta, Volume 201 (2022) no. 6, pp. 2797-2824 | DOI:10.1007/s10231-022-01219-5 | Zbl:1504.53027
  • J. Dubois; U. Hertrich-Jeromin; G. Szewieczek Notes on flat fronts in hyperbolic space, Journal of Geometry, Volume 113 (2022) no. 1, p. 13 (Id/No 20) | DOI:10.1007/s00022-022-00628-4 | Zbl:1491.53070
  • 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, pp. 505-546 | DOI:10.1007/s00229-018-1033-0 | Zbl:1412.53021
  • F. Burstall; U. Hertrich-Jeromin; W. Rossman Discrete linear Weingarten surfaces, Nagoya Mathematical Journal, Volume 231 (2018), pp. 55-88 | DOI:10.1017/nmj.2017.11 | Zbl:1411.53007
  • Udo Hertrich-Jeromin; Atsufumi Honda Minimal Darboux transformations, Beiträge zur Algebra und Geometrie, Volume 58 (2017) no. 1, pp. 81-91 | DOI:10.1007/s13366-016-0301-y | Zbl:1361.53011
  • Antonio Martínez; Pedro Roitman; Keti Tenenblat A connection between flat fronts in hyperbolic space and minimal surfaces in Euclidean space, Annals of Global Analysis and Geometry, Volume 48 (2015) no. 3, pp. 233-254 | DOI:10.1007/s10455-015-9468-y | Zbl:1405.53017
  • Alexander I. Bobenko; Udo Hertrich-Jeromin; Inna Lukyanenko Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality, Discrete Computational Geometry, Volume 52 (2014) no. 4, pp. 612-629 | DOI:10.1007/s00454-014-9622-5 | Zbl:1312.53011
  • Francis E. Burstall; Udo Hertrich-Jeromin; Wayne Rossman Lie geometry of linear Weingarten surfaces, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 350 (2012) no. 7-8, pp. 413-416 | DOI:10.1016/j.crma.2012.03.018 | Zbl:1252.53018

Cité par 10 documents. Sources : zbMATH

Commentaires - Politique

Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !

Publier un nouveau commentaire:

Publier une nouvelle réponse:

Ces articles pourraient vous intéresser

Lie geometry of linear Weingarten surfaces

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

C. R. Math (2012)