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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 6, Pages 1248–1264 (Mi smj1037)  
This article is cited in 31 scientific papers (total in 31 papers)

Surfaces in three-dimensional Lie groups

D. A. Berdinskiia, I. A. Taimanovb

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (298 kB) Citations (31)
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Abstract: We derive the Weierstrass (or spinor) representation for surfaces in the three-dimensional Lie groups Nil,$\widetilde{SL}_2$ , and Sol with Thurston's geometries and establish the generating equations for minimal surfaces in these groups. Using the spectral properties of the corresponding Dirac operators, we find analogs of the Willmore functional for surfaces in these geometries.
Keywords: surface, three-dimensional Lie group, Weierstrass representation, Willmore functional.
Received: 28.04.2005
English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 6, Pages 1005–1019
DOI: https://doi.org/10.1007/s11202-005-0096-9
Bibliographic databases:
UDC: 514.772.22
Language: Russian
Citation: D. A. Berdinskii, I. A. Taimanov, “Surfaces in three-dimensional Lie groups”, Sibirsk. Mat. Zh., 46:6 (2005), 1248–1264; Siberian Math. J., 46:6 (2005), 1005–1019
Citation in format AMSBIB
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\vol 46
\issue 6
\pages 1248--1264
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\zmath{https://zbmath.org/?q=an:1117.53045}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 6
\pages 1005--1019
\crossref{https://doi.org/10.1007/s11202-005-0096-9}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000234073700004}
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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