Central Projection of Hyperbolic Space onto a Horosphere
نویسندگان
چکیده
Horosphere is surface in hyperbolic space that is isometric to the Euclidean plane. In order to correctly visualize hyperbolic space we embed flat computer screen as horosphere and investigate geometry of central projection of hyperbolic space onto horosphere. We also discuss realization of hyperbolic isometries. Corresponding algorithms are implemented in Mathematica package L3toHorospere. We briefly present the package and obtain some interesting pictures of hyperbolic polyhedra.
منابع مشابه
On the Geometry of Constant Mean Curvature One Surfaces in Hyperbolic Space
We give a geometric classification of regular ends with constant mean curvature 1 and finite total curvature, embedded in hyperbolic space. We prove that each such end is either asymptotic to a catenoid cousin or asymptotic to a horosphere. We also study symmetry properties of constant mean curvature 1 surfaces in hyperbolic space associated to minimal surfaces in Euclidean space. We describe t...
متن کاملConfluence of Swallowtail Singularities of the Hyperbolic Schwarz Map Defined by the Hypergeometric Differential Equation
The papers [Gálvez et al. 2000, Kokubu et al. 2003, Kokubu et al. 2005] gave a method of constructing flat surfaces in the three-dimesnional hyperbolic space. Such surfaces have generically singularities, since any closed nonsigular flat surface is isometric to a horosphere or a hyperbolic cylinder. In the paper [Sasaki et al. 2006], we defined a map, called the hyperbolic Schwarz map, from the...
متن کاملExistence of constant mean curvature graphs in hyperbolic space
We give an existence result for constant mean curvature graphs in hyperbolic space Hn+1. Let Ω be a compact domain of a horosphere in Hn+1 whose boundary ∂Ω is mean convex, that is, its mean curvature H∂Ω (as a submanifold of the horosphere) is positive with respect to the inner orientation. If H is a number such that −H∂Ω < H < 1, then there exists a graph over Ω with constant mean curvature H...
متن کاملINTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS
In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.
متن کاملComplete Flat Surfaces with two Isolated Singularities in Hyperbolic 3 - space 1
We construct examples of flat surfaces in H3 which are graphs over a twopunctured horosphere and classify complete embedded flat surfaces in H3 with only one end and at most two isolated singularities. 2000 Mathematical Subject Classification: 53A35, 53C42
متن کامل