Rotational surfaces of constant astigmatism in space forms

Abstract

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.

To appear in Journal of Mathematical Analysis and Applications

References in corpus (2)

• On integrability of Weingarten surfaces: a forgotten class
• Visual Curve Completion and Rotational Surfaces of Constant Negative Curvature