Constant mean curvature tori in terms of elliptic functions.

Based on a numerical approximation of such a solution, we could produce plots of one ff-torus. In these Computer generated pictures the curvature lines for the smaller principal curvature λ^ looked almost planar. We then decided to restrict ourselves to fftori with one family of planar curvature lines. This condition translates into a second partial differential equation which induces a Separation of variables in the sinh-Gordon equation. Therefore the overdetermined System can be solved explicitly in terms of elliptic functions. We obtain a classification of all ff-tori in E which have one family of planar curvature lines.