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Zapiski Nauchnykh Seminarov POMI, 1996, Volume 234, Pages 65–124
(Mi znsl3631)
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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
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
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
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https://www.mathnet.ru/eng/znsl3631 https://www.mathnet.ru/eng/znsl/v234/p65
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Abstract page: | 120 | Full-text PDF : | 100 |
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