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SEMI-DISCRETE LINEAR WEINGARTEN SURFACES WITH WEIERSTRASS-TYPE REPRESENTATIONS AND THEIR SINGULARITIES

Yasumoto, Masashi 大阪大学 DOI:10.18910/73744

2020.01

概要

Lorentzian spaceforms are those for which the Gaussian and mean curvatures K and H
satisfy an affine linear relation
αK + 2βH + γ = 0
for constants α, β and γ not all zero, and generally these surfaces will have singularities.
There are special cases of these surfaces that admit Weierstrass-type representations:
(1) minimal surfaces in 3-dimensional Euclidean space R3 and their parallel surfaces,
(2) maximal surfaces in 3-dimensional Minkowski space R2,1 and their parallel surfaces,
(3) surfaces in 3-dimensional hyperbolic space H3 such that α = 1 − β and γ = −1 − β,
referred to here as linear Weingarten surfaces of Bryant type, or BrLW surfaces for
short (note that flat surfaces occur when β = 0),
(4) surfaces in 3-dimensional de Sitter space S2,1 such that α = −1 − β and γ = 1 − β,
referred to here as linear Weingarten surfaces of Bianchi type, or BiLW surfaces for
short.
The case of fully discrete surfaces with Weierstrass-type representations was considered
in [19], and the semi-discrete case is considered here. The semi-discrete case incorporates
2010 Mathematics Subject Classification. Primary 53A10; Secondary 52C99.
The first author was supported by the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Mathematical Science of Symmetry, Topology and Moduli,
Evolution of International Research Network based on OCAMI” (PI: Y. Ohnita). The second author was partly
supported by the Grant-in-Aid for Scientific Research (C) 15K04845 (PI: W. Rossman), and (S) 17H06127 (PI:
M.-H. Saito). ...

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参考文献

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Masashi Yasumoto

Osaka City University Advanced Mathematical Institute

3–3–138 Sugimoto, Sumiyoshi-ku Osaka 558–8585

Japan

e-mail: yasumoto@sci.osaka-cu.ac.jp

Wayne Rossman

Department of mathematics, Faculty of science

Kobe University

Rokkodai-cho 1–1, Nada-ku, Kobe, 657–8501

Japan

e-mail: wayne@math.kobe-u.ac.jp

...

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