Orthogonal curvilinear coordinate systems corresponding to singular spectral curves

Details Orthogonal curvilinear coordinate systems corresponding to singular spectral curves Orthogonal curvilinear coordinate systems corresponding to singular spectral curves

2006-01-04

arxiv.org/abs/math/0601062v3

Proc. Steklov Inst. Math. 255 (2006), 169-184

Mathematics

Differential Geometry

20 pages, 7 figures, minor typos corrected (first time the revised version was submiited in Russian)

Scientific paper

We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that the case when the curve is reducible and all its irreducible components are rational curves the construction procedure reduces to solving systems of linear equations and simple computations with elementary functions. Therewith we demonstrate how such well-known coordinate systems as the polar coordinates, the cylindrical coordinates in the three-space, and the spherical coordinates in the Euclidean spaces fit in this scheme.

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