Constant curvature rotational nets and periodic Bäcklund transforms

Abstract

After giving explicit parametrizations of discrete constant negative Gaussian curvature surfaces (negative CGC, i.e. discrete pseudospherical surfaces) of revolution, we construct Bäcklund transformations that again will have explicit parametrizations and are new examples of non-rotational discrete pseudospherical surfaces. In the process of doing this, for discrete CGC circular nets, we can provide rotationally invariant families of flat connections and give conditions on them so that the Bäcklund transformations preserve periodicity, that is, have annular topology.

26 pages, 8 figures