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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 223, Pages 69–78
DOI: https://doi.org/10.36535/0233-6723-2023-223-69-78
(Mi into1156)
 

Shadow problem and isometric embeddings of pseudospherical surfaces

A. V. Kostin

Elabuga Branch of Kazan (Volga Region) Federal University
References:
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.
Document Type: Article
UDC: 514.13
MSC: 53A35, 53B30
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Kos23}
\by A.~V.~Kostin
\paper Shadow problem and isometric embeddings of pseudospherical surfaces
\inbook 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
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 223
\pages 69--78
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1156}
\crossref{https://doi.org/10.36535/0233-6723-2023-223-69-78}
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