Multi-dimensional consistency of principal binets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908861465624576 |
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| author | Affolter, Niklas C. Techter, Jan |
| author_facet | Affolter, Niklas C. Techter, Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02449 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-dimensional consistency of principal binets Affolter, Niklas C. Techter, Jan Mathematical Physics Differential Geometry 53A70, 37J70, 51xxx 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. |
| title | Multi-dimensional consistency of principal binets |
| topic | Mathematical Physics Differential Geometry 53A70, 37J70, 51xxx |
| url | https://arxiv.org/abs/2603.02449 |