TY - JOUR
T1 - Semi-discrete linear weingarten surfaces with weierstrass-type representations and their singularities
AU - Yasumoto, Masashi
AU - Rossman, Wayne
N1 - Funding Information:
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).
Publisher Copyright:
© 2020, Osaka University. All rights reserved.
PY - 2020/1
Y1 - 2020/1
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:85078892315
SN - 0030-6126
VL - 57
SP - 169
EP - 185
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
IS - 1
ER -