# Discrete cyclic systems and circle congruences

@article{HertrichJeromin2022DiscreteCS, title={Discrete cyclic systems and circle congruences}, author={Udo Hertrich-Jeromin and Gudrun Szewieczek}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, year={2022} }

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…

## 4 Citations

### Notes on flat fronts in hyperbolic space

- MathematicsJournal of Geometry
- 2022

We give a short introduction to discrete flat fronts in hyperbolic space and prove that any discrete flat front in the mixed area sense admits a Weierstrass representation.

### Dupin cyclidic systems geometrically revisited

- Mathematics
- 2022

The induced metrics of Dupin cyclidic systems, that is, orthogonal coordinate systems with Dupin cyclides and spheres as coordinate surfaces, were provided by Darboux. Here we take a more geometric…

### Discrete Weierstrass-type representations.

- Mathematics
- 2021

Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type…

### Symmetry breaking in geometry

- Physics
- 2022

. A geometric mechanism that may, in analogy to similar notions in physics, be considered as “symmetry breaking” in geometry is described, and several instances of this mechanism in diﬀerential…

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