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arXiv · 2411.06413

On orthogonal curvilinear coordinate systems in constant curvature spaces

Dmitry Berdinsky·Ivan Rybnikov
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Abstract

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.

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Dmitry Berdinsky, Ivan Rybnikov. 2024-11-10. On orthogonal curvilinear coordinate systems in constant curvature spaces. https://arxiv.org/abs/2411.06413

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