On orthogonal curvilinear coordinate systems in constant curvature spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929586476941312 |
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| author | Berdinsky, Dmitry Rybnikov, Ivan |
| author_facet | Berdinsky, Dmitry Rybnikov, Ivan |
| contents | We describe a method for constructing $n$-orthogonal coordinate systems in constant curvature spaces. The construction proposed is a modification of Krichever's method for producing orthogonal curvilinear coordinate systems in the $n$-dimensional Euclidean space. To demonstrate how this method works, we construct examples of orthogonal coordinate systems on the two-dimensional sphere and the hyperbolic plane, in the case when the spectral curve is reducible and all irreducible components are isomorphic to a complex projective line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On orthogonal curvilinear coordinate systems in constant curvature spaces Berdinsky, Dmitry Rybnikov, Ivan Differential Geometry We describe a method for constructing $n$-orthogonal coordinate systems in constant curvature spaces. The construction proposed is a modification of Krichever's method for producing orthogonal curvilinear coordinate systems in the $n$-dimensional Euclidean space. To demonstrate how this method works, we construct examples of orthogonal coordinate systems on the two-dimensional sphere and the hyperbolic plane, in the case when the spectral curve is reducible and all irreducible components are isomorphic to a complex projective line. |
| title | On orthogonal curvilinear coordinate systems in constant curvature spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.06413 |