On a new definition of the Bäcklund transformation in the isometric deformation of surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916962382118912 |
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| author | Dinca, Ion I. |
| author_facet | Dinca, Ion I. |
| contents | We prove that a generic $4$-dimensional integrable rolling distribution of contact elements with the symmetry of the tangency configuration (excluding developable seed and isotropic developable leaves) splits into an $1$-dimensional family of generic $3$-dimensional integrable rolling distributions of contact elements with the symmetry of the tangency configuration, thus introducing a new definition of the Bäcklund transformation in the isometric deformation of surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01135 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a new definition of the Bäcklund transformation in the isometric deformation of surfaces Dinca, Ion I. Differential Geometry We prove that a generic $4$-dimensional integrable rolling distribution of contact elements with the symmetry of the tangency configuration (excluding developable seed and isotropic developable leaves) splits into an $1$-dimensional family of generic $3$-dimensional integrable rolling distributions of contact elements with the symmetry of the tangency configuration, thus introducing a new definition of the Bäcklund transformation in the isometric deformation of surfaces. |
| title | On a new definition of the Bäcklund transformation in the isometric deformation of surfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.01135 |