Question

This question deals with the upper half plane model of hyperbolic geometry. Points are
represented by complex numbers with positive imaginary component. Define what it meant
by saying that two hyperbolic lines l and m are parallel. Does a pair of parallel lines necessarily
have a common perpendicular? If not, state a simple criterion for one to exist.
For each of the following pairs of hyperbolic lines, l and m, state whether or not they have a
common perpendicular and if so determine what it is.
(i) l = {z ∈ H | Re(z) = −1} and m = {z ∈ H | Re(z) = 2}.

Answer 1

http://en.wikipedia.org/wiki/Ultraparallel_theorem

Answer 2

http://uk.answers.yahoo.com/question/index?qid=20110515063415AAwDlEI