E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
Annali di Matematica Pura ed Applicata
Number of Pages:
Cyclic circle congruence; Cyclic system; Discrete differential geometry; Discrete flat front; Dupin cyclide; Lie sphere geometry; Möbius geometry; Normal line congruence; Orthogonal coordinate system
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail and characterized by the existence of a certain flat connection. Within the developed framework, discrete cyclic systems with a family of discrete flat fronts in hyperbolic space and discrete cyclic systems, where all coordinate surfaces are discrete Dupin cyclides, are investigated.