Multi-dimensional consistency of principal binets
Abstract
Principal binets are a discretization of curvature line parametrized surfaces defined on the vertices and faces of the square lattice Z 2 . They generalize the previously established discretizations given by circular nets, conical nets, and principal contact element nets. We show that principal binets constitute a discrete integrable system in the sense of multi-dimensional consistency. In particular, they generalize to higher-dimensional square lattices Z N . We also discuss relations to the notion of discrete orthogonal coordinate systems as previously established for discrete confocal quadrics.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Mathematics and Applications
Publication details
- Journal / source
- Journal of Geometry and Physics
- Volume
- 230
- Pages
- 105991–105991
- Publication date
- 26 August 2026
- Language
- EN