  A surface in a Riemannian space is called of constant astigmatism if the
difference between the principal radii of curvatures at each point is a
constant function. In this paper we give a classification of all rotational
surfaces of constant astigmatism in space forms. We also prove that the
generating curves of such surfaces are critical points of a variational problem
for a curvature energy. Using the description of these curves, we locally
construct all rotational surfaces of constant astigmatism as the associated
binormal evolution surfaces from the generating curves.
