  The Groups of causal and conformal automorphisms of globally hyperbolic
spacetimes were studied.
  In two dimensions, we prove that all globally hyperbolic spacetimes that are
directed and connected are causally isomorphic. We work out the consequences of
this fact and obtain a (partial) classification of the causal automorphism and
conformal groups of a two-dimensional globally hyperbolic space.
  Finally, we present a generalization for locally conformally flat globally
hyperbolic spacetimes.
