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Tr. Mat. Inst. Steklova, 1999, Volume 225, Pages 21–45 (Mi tm711)  

This article is cited in 20 scientific papers (total in 20 papers)

Discrete Analogs of the Darboux–Egorov Metrics

A. A. Akhmetshinab, Yu. S. Vol'vovskiiab, I. M. Kricheverab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Columbia University

Abstract: A discrete analog of the Darboux–Egorov metrics is constructed and the geometry of the corresponding lattices in a Euclidean space is shown to be described by the set of functions $h_i^{\pm}(u)$, $u\in\mathbb Z^n$. A discrete analog of the Lamé equations is determined, and it is shown that these equations are necessary and sufficient for the solutions to this analog to be the rotation coefficients of the Darboux–Egorov lattice up to a gauge transformation. A scheme for the construction of explicit solutions to the discrete Lamé equations in terms of the Riemann $\theta$-functions is presented.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 225, 16–39

Bibliographic databases:
UDC: 517.9
Received in December 1998

Citation: A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever, “Discrete Analogs of the Darboux–Egorov Metrics”, Solitons, geometry, and topology: on the crossroads, Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov, Tr. Mat. Inst. Steklova, 225, Nauka, MAIK Nauka/Inteperiodika, M., 1999, 21–45; Proc. Steklov Inst. Math., 225 (1999), 16–39

Citation in format AMSBIB
\Bibitem{AkhVolKri99}
\by A.~A.~Akhmetshin, Yu.~S.~Vol'vovskii, I.~M.~Krichever
\paper Discrete Analogs of the Darboux--Egorov Metrics
\inbook Solitons, geometry, and topology: on the crossroads
\bookinfo Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov
\serial Tr. Mat. Inst. Steklova
\yr 1999
\vol 225
\pages 21--45
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm711}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1725931}
\zmath{https://zbmath.org/?q=an:0980.37028}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 225
\pages 16--39


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