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Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 354–360 (Mi semr592)  

This article is cited in 1 scientific paper (total in 1 paper)

Geometry and topology

Casey's theorem in hyperbolic geometry

N. V. Abrosimovabc, L. A. Mikaiylovaa

a Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia
b Laboratory of Quantum Topology, Chelyabinsk State University, Brat’ev Kashirinykh st., 129, 454001, Chelyabinsk, Russia
c Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We obtain a hyperbolic version of Casey's theorem. A similar result is obtained in spherical geometry as well.

Keywords: Casey's theorem, Ptolemy's theorem, hyperbolic plane, spherical plane.

DOI: https://doi.org/10.17377/semi.2015.12.029

Full text: PDF file (128 kB)
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UDC: 514.13
MSC: 51M09
Received May 26, 2015, published June 9, 2015
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Citation: N. V. Abrosimov, L. A. Mikaiylova, “Casey's theorem in hyperbolic geometry”, Sib. Èlektron. Mat. Izv., 12 (2015), 354–360

Citation in format AMSBIB
\Bibitem{AbrMik15}
\by N.~V.~Abrosimov, L.~A.~Mikaiylova
\paper Casey's theorem in hyperbolic geometry
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 354--360
\mathnet{http://mi.mathnet.ru/semr592}
\crossref{https://doi.org/10.17377/semi.2015.12.029}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kostin, N. N. Kostina, “Interpretatsii teoremy Kezi i ee giperbolicheskogo analoga”, Sib. elektron. matem. izv., 13 (2016), 242–251  mathnet  crossref
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