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Zapiski Nauchnykh Seminarov POMI, 1996, Volume 234, Pages 65–124 (Mi znsl3631)  
This article is cited in 8 scientific papers (total in 8 papers)

On some integrable cases in surface theory

D. A. Korotkin

II Institute for Theoretical Physics, Hamburg University
Full-text PDF (2155 kB) Citations (8)
Abstract: It is shown how to reformulate the Gauss–Codazzi system for a surface with arbitrary Gaussian curvature in the form of one second-order differential equation. A similar reformulation is performed for a surface with fixed mean curvature. In the cases of two-dimensional Bianchi surfaces of positive curvature, these equations correspond to the unitary reduction of the coupled Ernst system of the equations of general gravity.
The theta-functional description of the corresponding geometric objects is given. Bibl. 22 titles.
Received: 20.10.1992
English version:
Journal of Mathematical Sciences (New York), 1999, Volume 94, Issue 2, Pages 1177–1217
DOI: https://doi.org/10.1007/BF02364876
Bibliographic databases:
Document Type: Article
UDC: 517.934
Language: English
Citation: D. A. Korotkin, “On some integrable cases in surface theory”, Differential geometry, Lie groups and mechanics. Part 15–1, Zap. Nauchn. Sem. POMI, 234, POMI, St. Petersburg, 1996, 65–124; J. Math. Sci. (New York), 94:2 (1999), 1177–1217
Citation in format AMSBIB
\Bibitem{Kor96}
\by D.~A.~Korotkin
\paper On some integrable cases in surface theory
\inbook Differential geometry, Lie groups and mechanics. Part~15--1
\serial Zap. Nauchn. Sem. POMI
\yr 1996
\vol 234
\pages 65--124
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3631}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1856079}
\zmath{https://zbmath.org/?q=an:0964.53007}
\transl
\jour J. Math. Sci. (New York)
\yr 1999
\vol 94
\issue 2
\pages 1177--1217
\crossref{https://doi.org/10.1007/BF02364876}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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