Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- 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
Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms
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.
Received: 13 October 2015
Revised: 29 September 2016
First available in Project Euclid: 4 October 2018
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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