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Sibirsk. Mat. Zh., 2011, Volume 52, Number 3, Pages 502–511 (Mi smj2215)  

This article is cited in 2 scientific papers (total in 2 papers)

On orthogonal curvilinear coordinate systems in constant curvature spaces

D. A. Berdinskii, I. P. Rybnikov

Novosibirsk State University, Novosibirsk

Abstract: We describe a method for constructing an $n$-orthogonal coordinate system in constant curvature spaces. The construction proposed is actually a modification of the Krichever method for producing an orthogonal coordinate system in the $n$-dimensional Euclidean space. To demonstrate how this method works, we construct some examples of orthogonal coordinate systems on the twodimensional 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.

Keywords: orthogonal coordinate systems, spaces of constant curvature, Baker–Akhiezer function.

Full text: PDF file (400 kB)
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English version:
Siberian Mathematical Journal, 2011, 52:3, 394–401

Bibliographic databases:

UDC: 517.957
Received: 28.09.2010

Citation: D. A. Berdinskii, I. P. Rybnikov, “On orthogonal curvilinear coordinate systems in constant curvature spaces”, Sibirsk. Mat. Zh., 52:3 (2011), 502–511; Siberian Math. J., 52:3 (2011), 394–401

Citation in format AMSBIB
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\by D.~A.~Berdinskii, I.~P.~Rybnikov
\paper On orthogonal curvilinear coordinate systems in constant curvature spaces
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 3
\pages 502--511
\mathnet{http://mi.mathnet.ru/smj2215}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858638}
\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 3
\pages 394--401
\crossref{https://doi.org/10.1134/S0037446611030025}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959783620}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. I. Mokhov, “O metrikakh diagonalnoi krivizny”, Fundament. i prikl. matem., 21:6 (2016), 171–182  mathnet
    2. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Russian Math. Surveys, 72:5 (2017), 889–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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