horosphere means 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. Lexicurio rates it Sui generis — a strength score of 90 out of 100.
Etymology
A modern scientific coinage, probably from a Latinized spelling of Ancient Greek ὅρος (hóros, “boundary”) (not to be confused with ὧρος (hôros, “year”), which gave rise to many time-related terms) + -sphere
noun
- 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.