The Bäcklund Transform of Principal Contact Element Nets

Details The Bäcklund Transform of Principal Contact Element Nets The Bäcklund Transform of Principal Contact Element Nets

2010-10-16

arxiv.org/abs/1010.3339v1

Mathematics

Differential Geometry

Minor corrections and clarifications

Scientific paper

We investigate geometric aspects of the the B\"acklund transform of principal contact element nets. A B\"acklund transform exists if and only if it the principal contact element net is of constant negative Gaussian curvature (a pseudosphere). We describe an elementary construction of the B\"acklund transform and prove its correctness. Finally, we show that Bianchi's Permutation Theorem remains valid in our discrete setting.

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