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Ivory's Theorem in Hyperbolic Spaces

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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.

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Authors and Affiliations

  1. Technische Universitat Wien, U.S.A

    H. Stachel & J. Wallner

Authors
  1. H. Stachel
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  2. J. Wallner
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Stachel, H., Wallner, J. Ivory's Theorem in Hyperbolic Spaces. Siberian Mathematical Journal 45, 785–794 (2004). https://doi.org/10.1023/B:SIMJ.0000035839.90234.45

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000035839.90234.45

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