Namespaces
Variants
Actions

Horosphere

From Encyclopedia of Mathematics
Revision as of 17:27, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

orisphere

A surface in Lobachevskii space, orthogonal to (hyperbolic) parallel straight lines in a certain direction. A horosphere can be considered as a sphere with centre at infinity. A Euclidean geometry can be realized on a horosphere if straight lines are taken to be horocycles (cf. Horocycle), the order of the points is defined through the order of the straight lines in the pencil of parallels defining the horocycle, and a motion is taken to be a motion in Lobachevskii space that takes the horosphere onto itself.


Comments

References

[a1] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1961)
[a2] A.P. Norden, "Elementare Einführung in die Lobatschewskische Geometrie" , Deutsch. Verlag Wissenschaft. (1958) (Translated from Russian)
How to Cite This Entry:
Horosphere. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Horosphere&oldid=18806
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article