Equidistant Surfaces in H^2×R Space

Sa？etak After having investigated the equidistant surfaces (”perpendicular bisectors” of two points) in S^2×R space (see[6]) we consider the analogous problem in H^2×R space from among the eight Thurston geometries. In [10] the third author has determined the geodesic curves, geodesic balls of H^2×R space and has computed their volume, has defined the notion of the geodesic ball packing and its density. Moreover, he has developed a procedure to determine the density of the geodesic ball packing for generalized Coxeter space groups of H^2×R and he has applied this algorithm to them. In this paper we introduce the notion of the equidistant surface to two points in H^2×R geometry, determine its equation and we shall visualize it in some cases. The pictures have been made by the Wolfram Mathematica software