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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 1995, Volume 2, Number 3, Pages 319–328
(Mi jmag635)
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On construction of isometric immersions of the domains of Lobachevsky plane $L^2$ into $E^4$
by using solutions of the “sine-Gordon” equation
O. V. Kuznetsov Kharkiv State University
Abstract:
Isometric immersions of the Lobachevsky plane $L^2$ into $E^4$, are considered. These immersions are surfaces in $E^4$, which have a vanishing Gaussian torsion. The immersions are constructed by using different solutions of the “sine-Gordon” equation. It is proved that the domains of $L^2$, which are immersed, are parts of the domains bounded by two horocycles or two equidistants. The sizes of the domains under consideration are estimated.
Received: 23.02.1994
Citation:
O. V. Kuznetsov, “On construction of isometric immersions of the domains of Lobachevsky plane $L^2$ into $E^4$
by using solutions of the “sine-Gordon” equation”, Mat. Fiz. Anal. Geom., 2:3 (1995), 319–328
Linking options:
https://www.mathnet.ru/eng/jmag635 https://www.mathnet.ru/eng/jmag/v2/i3/p319
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Abstract page: | 69 | Full-text PDF : | 33 |
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