Gaussian and mean curvatures for discrete asymptotic nets

JOURNAL OF GEOMETRY AND PHYSICS

卷:114

Article

Schief, W. K.^1,2 

[1] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Univ New South Wales, Sch Math & Stat, Ctr Excellence Math & Stat Complex Syst, Australian Res Council, Sydney, NSW 2052, Australia

关键词: Discrete differential geometry;    Integrable systems;   

DOI  :  10.1016/j.geomphys.2016.11.031

来源: Elsevier

【 摘 要 】

We propose discretisations of Gaussian and mean curvatures of surfaces parametrised in terms of asymptotic coordinates and examine their relevance in the context of integrable discretisations of classical classes of surfaces and their underlying integrable systems. We also record discrete analogues of the classical relation between the Gaussian curvature of hyperbolic surfaces and the torsion of their asymptotic lines. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free