Rotational surfaces of constant astigmatism in space forms

Abstract A surface in a Riemannian space is called surface of constant astigmatism if the difference between the principal radii of curvature 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 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.