This article is cited in 11 papers

Ivory's theorem in hyperbolic spaces

H. Stachel, J. Wallner

Vienna University of Technology

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.

UDC: 514.13, 514.144.24

Received: 09.10.2003

 English version: Siberian Mathematical Journal, 2004, 45:4, 785–794

Bibliographic databases:

• 
• 
•