horosphere
An -dimensional hyperplane in hyperbolic -dimensional space: it is (in the Poincaré disk) Euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) Euclidean-parallel to the boundary hyperplane.

Wikipedia foundation.

Look at other dictionaries:

  • Horoball — In mathematics, particularly hyperbolic geometry, a horoball is a specific kind of n dimensional object in hyperbolic n space. Consider the upper half space model of hyperbolic space. Then a horosphere is given by a horizontal plane, and the… …   Wikipedia

  • Non-Euclidean geometry — Behavior of lines with a common perpendicular in each of the three types of geometry Non Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate,… …   Wikipedia

  • Glossary of Riemannian and metric geometry — This is a glossary of some terms used in Riemannian geometry and metric geometry mdash; it doesn t cover the terminology of differential topology. The following articles may also be useful. These either contain specialised vocabulary or provide… …   Wikipedia

  • Anosov diffeomorphism — In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of expansion and contraction .… …   Wikipedia

  • Horocycle — A blue horocycle in the Poincaré disk model and some red normals. The normals converge asymptotically to the upper central point. In hyperbolic geometry, a horocycle (Greek: όριο + κύκλος border + circle) is a curve whose normals all converge… …   Wikipedia

  • Lexique de la géométrie riemannienne — La géométrie riemannienne est un domaine des mathématiques étudiant les propriétés des variétés riemanniennes. Cette page rappelle brièvement les définitions des termes récurrents rencontrés. Sommaire : Haut A B C D E F G H I J K L M N O P Q …   Wikipédia en Français

  • horoball — noun A horosphere together with the space above it …   Wiktionary

  • horospherical — adjective Of or pertaining to a horosphere …   Wiktionary

  • Horobola — Este artículo o sección necesita referencias que aparezcan en una publicación acreditada, como revistas especializadas, monografías, prensa diaria o páginas de Internet fidedignas. Puedes añadirlas así o avisar al autor prin …   Wikipedia Español

  • horo- — ♦ Élément, du gr. hôro , de hôra « heure ». I. ⇒HORO 1, élém. formant Élém. tiré du gr. , de « heure », entrant dans la formation de qq. subst. et adj., dans différents domaines : horodateur, horo dateur, trice, subst. masc. et adj. « (Appareil)… …   Encyclopédie Universelle

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”