Rotational surfaces of constant astigmatism in space forms
Differential Geometry
2020-05-18 v1
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.
Keywords
Cite
@article{arxiv.2005.07689,
title = {Rotational surfaces of constant astigmatism in space forms},
author = {Rafael López and Álvaro Pámpano},
journal= {arXiv preprint arXiv:2005.07689},
year = {2020}
}
Comments
To appear in Journal of Mathematical Analysis and Applications