J. Phys. I France
Volume 3, Numéro 3, March 1993
Page(s) 839 - 854
DOI: 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. Sadoc

Laboratoire 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)

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.

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