Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3-space
Differential Geometry
2017-09-22 v2
Abstract
We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean curvature 1 surfaces in hyperbolic 3-space, and we also describe discrete focal surfaces (discrete caustics) that can be used to define singularities on discrete flat surfaces. We also examine discrete linear Weingarten surfaces of Bryant type in hyperbolic 3-space, and consider an example of a discrete flat surface related to the Airy equation that exhibits swallowtail singularities and a Stokes phenomenon.
Cite
@article{arxiv.0912.4972,
title = {Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3-space},
author = {Tim Hoffmann and Wayne Rossman and Takeshi Sasaki and Masaaki Yoshida},
journal= {arXiv preprint arXiv:0912.4972},
year = {2017}
}
Comments
version 2: minor typos corrected, one sentence in proof of Lemma 6.5 revised, results unchanged