Rotational surfaces of constant astigmatism in space forms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Lopez, Rafael¹  Pampano, Alvaro² 

[1] Univ Granada, Inst Matemat IEMath GR, Dept Geometria & Topol, E-18071 Granada, Spain

[2] Univ Basque Country, Fac Sci & Technol, Dept Math, Bilbao 48940, Spain

关键词: Surface of constant astigmatism;    Critical curve;    Spherical rotational surface;    Binomial evolution surface;   

DOI  :  10.1016/j.jmaa.2019.123602

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free