Discrete differential geometry. Integrability as consistency
نویسنده
چکیده
Since ‘nice’ and ‘interesting’ can hardly be treated as mathematically formulated features, let us discuss the permutability property. We shall explain it in more detail for the classical example of surfaces with constant negative Gaussian curvature (K-surface) with their Bäcklund transformations. Let r : R → R be a K-surface, and r10 and r01 two K-surfaces obtained by Bäcklund transformations of r. The classical Bianchi permutability theorem claims that there exists a unique K-surface r11 which is a Bäcklund transform of r10 and r01. Moreover, (i) the straight line connecting the points r(x, y)and r10(x, y) lies in the tangent planes of the surfaces r and r10 at these points,
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