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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 4, Pages 946–959 (Mi smj1115)  
This article is cited in 11 scientific papers (total in 11 papers)

Ivory's theorem in hyperbolic spaces

H. Stachel, J. Wallner

Vienna University of Technology
Full-text PDF (391 kB) Citations (11)
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Abstract: According to the planar version of Ivory's theorem, the family of confocal conics has the property that in each curvilinear quadrangle formed by two pairs of conics the diagonals are of equal length. It turned out that this theorem is closely related to selfadjoint affine transformations. This point of view opens up a possibility of generalizing the Ivory theorem to the hyperbolic and other spaces.
Keywords: hyperbolic geometry, Ivory's theorem, confocal quadrics.
Received: 09.10.2003
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 4, Pages 785–794
DOI: https://doi.org/10.1023/B:SIMJ.0000035839.90234.45
Bibliographic databases:
UDC: 514.13, 514.144.24
Language: Russian
Citation: H. Stachel, J. Wallner, “Ivory's theorem in hyperbolic spaces”, Sibirsk. Mat. Zh., 45:4 (2004), 946–959; Siberian Math. J., 45:4 (2004), 785–794
Citation in format AMSBIB
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\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 4
\pages 785--794
\crossref{https://doi.org/10.1023/B:SIMJ.0000035839.90234.45}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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