Kennzeichnungen hyperbolischer Bewegungen durch Lineationen

LetI n be the set of points ofn-dimensional hyperbolic geometry,n≥2. THEOREM 1. Letf∶I n →I n be a surjection such that images of hyperbolic lines are contained in hyperbolic lines. Thenf is a hyperbolic motion. THEOREM 2. Iff∶In→In maps hyperbolic lines onto hyperbolic lines, then the image off is a hyperbolic line, orf is a hyperbolic motion. We note that Theorem 1 is a consequence of [3, Theorem 2.4].