The B\"acklund Transform of Principal Contact Element Nets
Differential Geometry
2010-10-19 v1 Metric Geometry
Abstract
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.
Cite
@article{arxiv.1010.3339,
title = {The B\"acklund Transform of Principal Contact Element Nets},
author = {Hans-Peter Schröcker},
journal= {arXiv preprint arXiv:1010.3339},
year = {2010}
}
Comments
Minor corrections and clarifications