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 
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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

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