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January 2020 Semi-discrete linear Weingarten surfaces with Weierstrass-type representations and their singularities
Masashi Yasumoto, Wayne Rossman
Osaka J. Math. 57(1): 169-185 (January 2020).

Abstract

We establish what semi-discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms are, confirming their required properties regarding curvatures and parallel surfaces, and then classify them. We then define and analyze their singularities. In particular, we discuss singularities of (1) semi-discrete surfaces with non-zero constant Gaussian curvature, (2) parallel surfaces of semi-discrete minimal and maximal surfaces, and (3) semi-discrete constant mean curvature $1$ surfaces in de Sitter $3$-space. We include comparisons with different previously known definitions of such singularities.

Citation

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Masashi Yasumoto. Wayne Rossman. "Semi-discrete linear Weingarten surfaces with Weierstrass-type representations and their singularities." Osaka J. Math. 57 (1) 169 - 185, January 2020.

Information

Published: January 2020
First available in Project Euclid: 15 January 2020

zbMATH: 07196622
MathSciNet: MR4052635

Subjects:
Primary: 53A10
Secondary: 52C99

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics

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Vol.57 • No. 1 • January 2020
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