Orthogonal curvilinear coordinate systems corresponding to singular spectral curves
Differential Geometry
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0601062,
title = {Orthogonal curvilinear coordinate systems corresponding to singular spectral curves},
author = {A. E. Mironov and I. A. Taimanov},
journal= {arXiv preprint arXiv:math/0601062},
year = {2007}
}
Comments
20 pages, 7 figures, minor typos corrected (first time the revised version was submiited in Russian)