Abstract
Many geometers in the 19th and early 20th century studied surfaces in R 3 with particular conditions on the curvature. Examples include minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature. The typical observation was that one could introduce a special coordinate chart (i.e. curvature lines or asymptotic lines) in order to reduce the compatability conditions of the given class of surfaces to some nonlinear P.D.E. In this way, the description of a given class of surfaces is reduced to the study of the solution space of the corresponding P.D.E. The following table illustrates this correspondence. Here, the compatability conditions are given in curvature line coordinates.
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