2015/10/22 by Tim Hoffmann, Hoffmann, Tim, Andrew O. Sageman‐Furnas +2
Engineering · Mathematics · Physics and Astronomy · #37K25 #37K35 #53A05 #Advanced Differential Geometry Research #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #math.DG #msc:37K25 #msc:37K35 #msc:53A05
paper · pdf · doi:10.48550/arxiv.1510.06654
arxiv created 2015/10/22 · openalex publication_date 2015/10/22 · arxiv updated 2015/10/23 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28
We present a 2x2 Lax representation for discrete circular nets of constant negative Gauß curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete K-nets (in asymptotic line parametrization). The description gives rise to Bäcklund transformations and an associated family. All the members of that family -- although no longer circular -- can be shown to have constant Gauß curvature as well. Explicit solutions for the Bäcklund transformations of the vacuum (in particular Dini's surfaces and breather solutions) and their respective associated families are given.