Rotational surfaces in H_3 with constant Gauss curvature

invariant by rotations about the z-axis. Here one finds a complete description of all rotational surfaces with constant Gauss curvatureK in the Heisenberg space H3. Despite many and substantial similarities with the Euclidean case, this family of surfaces displays some phenomena which do not have their counterpart in R. For K = 0 there are three cases, for K > 0 also three cases, but for K < 0 five cases. The profile curves of all these cases are illustrated on the corresponding figures and characterized geometrically.