2010/10/16 by Hans-Peter Schröcker, Schröcker, Hans-Peter
Engineering · Mathematics · #53A05 #53A17 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.DG #math.MG #msc:53A05 #msc:53A17
paper · pdf · doi:10.48550/arxiv.1010.3339
Minor corrections and clarifications
arxiv created 2010/10/16 · openalex publication_date 2010/10/16 · arxiv updated 2010/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate geometric aspects of the the Bäcklund transform of principal contact element nets. A Bäcklund 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 Bäcklund transform and prove its correctness. Finally, we show that Bianchi's Permutation Theorem remains valid in our discrete setting.