horosphere

Etymology
A modern scientific coinage, probably from a Latinized spelling of (not to be confused with, which gave rise to many time-related terms) +

Noun

 * 1) An $$n-1$$-dimensional hyperplane in hyperbolic $$n$$-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.