Advanced Studies in Pure Mathematics

Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms

Wayne Rossman and Masashi Yasumoto

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper we define and analyze singularities of discrete linear Weingarten surfaces with Weierstrass-type representations in 3-dimensional Riemannian and Lorentzian spaceforms. In particular, we discuss singularities of discrete surfaces with non-zero constant Gaussian curvature, and parallel surfaces of discrete minimal and maximal surfaces, and discrete constant mean curvature 1 surfaces in de Sitter 3-space, including comparisons with different previously known definitions of such singularities.

Article information

Singularities in Generic Geometry, S. Izumiya, G. Ishikawa, M. Yamamoto, K. Saji, T. Yamamoto and M. Takahashi, eds. (Tokyo: Mathematical Society of Japan, 2018), 383-410

Received: 13 October 2015
Revised: 29 September 2016
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538618983

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 52C99: None of the above, but in this section

discrete differential geometry Weierstrass-type representation singularity


Rossman, Wayne; Yasumoto, Masashi. Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms. Singularities in Generic Geometry, 383--410, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07810383.

Export citation