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Bbstract Geometric relations linking the (local) molecular shape of the aggregating surfactant molecules to the (global) composition of the surfactant-water mixture. The presence of cubic, tetragonal and rhombohedra1 phases is suggested to be due to the formation of hyperbolic interfaces, of minimum bending energy.

Description de structures interpenetrantes en utilisant des surfaces paralleles minimales periodiques, decrites par geometrie differentielle. Exemples de composes dont les structures sont decrites en utilisant ces surfaces. Explication par le concept de courbure, d'une description geometrique de la liaison chimique, de l'absorption selective de gaz par des zeolites, ainsi qu'un nouveau mecanisme de craquage catalytique de petrole

Mise en evidence, dans le systeme eau-monooleine, d'une transition d'une structure cubique centree de type gyroide en une structure cubique a reseau simple avec une couche de lipide formant une surface infinie minimale et periodique de type diamant. Determination des caracteristiques et de la nature d'une telle transformation. Etablissement du diagramme de phase du systeme eau-monooleine

The use of space group stereohedra derived by Bashkirov as free boundaries result in a multiplicity of intersection-free (as well as self-intersecting) translationally periodic minimal surfaces of that space group. Surface solutions have differing tunnel networks and curvature, distinguished by their topology. The exact geometry of these surfaces can be calculated by constructing a function which depends only on the surface normal vectors at flat points on the surface, and solving the Weierstrass equations. Translationally periodic surfaces of constant average curvature can be determined from the periodic minimal surface solutions. Some examples of the various techniques for calculating the geometry and topology of these periodic surfaces are given