Area preserving Combescure transformations
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912339237797888 |
|---|---|
| author | Pirahmad, O. Pottmann, H. Skopenkov, M. |
| author_facet | Pirahmad, O. Pottmann, H. Skopenkov, M. |
| contents | Motivated by the design of flexible nets, we classify all nets of arbitrary size m x n that admit a continuous family of area-preserving Combescure transformations. There are just two different classes. The nets in the first class are special cases of cone nets that have been recently studied by Kilian, Mueller, and Tervooren. The second class consists of Koenigs nets having a Christoffel dual with the same areas of corresponding faces. We apply isotropic metric duality to get a new class of flexible nets in isotropic geometry. We also study the smooth analogs of the introduced classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Area preserving Combescure transformations Pirahmad, O. Pottmann, H. Skopenkov, M. Metric Geometry Differential Geometry 53A70, 53A05, 52C25, 53A35 Motivated by the design of flexible nets, we classify all nets of arbitrary size m x n that admit a continuous family of area-preserving Combescure transformations. There are just two different classes. The nets in the first class are special cases of cone nets that have been recently studied by Kilian, Mueller, and Tervooren. The second class consists of Koenigs nets having a Christoffel dual with the same areas of corresponding faces. We apply isotropic metric duality to get a new class of flexible nets in isotropic geometry. We also study the smooth analogs of the introduced classes. |
| title | Area preserving Combescure transformations |
| topic | Metric Geometry Differential Geometry 53A70, 53A05, 52C25, 53A35 |
| url | https://arxiv.org/abs/2402.16753 |