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Shadow problem and isometric embeddings of pseudospherical surfaces
A. V. Kostin Elabuga Branch of Kazan (Volga Region) Federal University
Abstract:
The shadow problem for horospheres is related to the problem of global isometric embedding of surfaces of revolution of constant negative curvature into the three-dimensional Euclidean space. Euclidean surfaces of revolution of constant negative curvature are globally isometric to parts of tangent cones of horospheres in the three-dimensional Lobachevsky space. In this work, meridians of Euclidean pseudospherical surfaces of revolution are expressed in terms of metric characteristics in the hyperbolic space, namely, in terms of the distance from the vertex of the tangent cone to the horosphere or through the distance from the polar of the vertex to the horosphere.
Keywords:
shadow problem, surface of constant curvature, pseudosphere, horosphere, Lobachevsky space.
Citation:
A. V. Kostin, “Shadow problem and isometric embeddings of pseudospherical surfaces”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 223, VINITI, Moscow, 2023, 69–78
Linking options:
https://www.mathnet.ru/eng/into1156 https://www.mathnet.ru/eng/into/v223/p69
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Abstract page: | 94 | Full-text PDF : | 62 | References: | 27 |
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