Advanced Studies in Pure Mathematics

Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms

Wayne Rossman and Masashi Yasumoto

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Abstract

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

Source
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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538618983

Digital Object Identifier
doi:10.2969/aspm/07810383

Mathematical Reviews number (MathSciNet)
MR3839955

Zentralblatt MATH identifier
07085113

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

Keywords
discrete differential geometry Weierstrass-type representation singularity

Citation

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. https://projecteuclid.org/euclid.aspm/1538618983


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