Siberian Mathematical Journal

, Volume 45, Issue 4, pp 785–794 | Cite as

Ivory's Theorem in Hyperbolic Spaces

  • H. Stachel
  • J. Wallner


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.

hyperbolic geometry Ivory's theorem confocal quadrics 


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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • H. Stachel
    • 1
  • J. Wallner
    • 1
  1. 1.Technische Universitat WienU.S.A

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