The global spatial requirement set by the composition of a binary surfactant-water system can be expressed as a function of the local intrinsic geometry of the surfactant film, assuming a reasonably homogeneous film, which is equivalent to a film of low bending energy. These relations are calculated for (quasi-)homogeneous hyperbolic, elliptic (spheres) and parabolic (cylinders) geometries. It is suggested that the crystallinity of some surfactant mesophases is a result of the homogeneity constraint. Detailed theory of structures found in bicontinuous cubic phases, as well as experimental techniques for deciphering the microstructure of these phases is presented