Issue |
J. Phys. I France
Volume 3, Number 3, March 1993
|
|
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Page(s) | 839 - 854 | |
DOI | https://doi.org/10.1051/jp1:1993166 |
J. Phys. I France 3 (1993) 839-854
Crystallographic aspects of the Bonnet transformation for periodic minimal surfaces (and crystals of films)
C. Oguey and J.-F. SadocLaboratoire de Physique des Solides, Bât. 510, Université de Paris-Sud, F-91405 Orsay, France
(Received 2 July 1992, accepted in final form 29 October 1992)
Abstract
The surfaces with vanishing mean curvature, or minimal surfaces, are linear projections of minimal surfaces imbedded in the
complex 3 dimensional space C
3. For real minimal surfaces, the Bonnet transformations form a one parameter group of isometries which correspond to generalised
rotations in the complex or higher dimensional space. The translation symmetries of fully periodic minimal surfaces in both
R
3 and C
3 are investigated, with emphasis on the example of the P, D and G surfaces. The relevance of the Bonnet transformation for
physical transitions is then discussed in the light of higher dimensional crystallography.
02.40 - 61.50K - 68.00
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