TY - JOUR
T1 - Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space
AU - Honda, Atsufumi
AU - Koiso, Miyuki
AU - Saji, Kentaro
N1 - Funding Information:
and Kotaro Yamada for valuable commen ts. The first and the second authors are partially supported by Gran t-in-Aid for Challenging Exploratory Researc h No. 26610016 of the Japan Societ y for the Promotion of Science. The second author is partially supported by Gran t-in-Aid for Scien tific Re-searc h (B) No. 25287012 and the third author by (C) No. 26400087 from Japan Societ y for the Promotion of Science.
Publisher Copyright:
© 2013 Department of Mathematics, Hokkaido University.
PY - 2018
Y1 - 2018
N2 - Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular points on spacelike surfaces with non-zero constant mean curvature (spacelike CMC surfaces). We prove that spacelike CMC surfaces do not admit fold singular points. Moreover, we show that the singular point set of any conjugate CMC surface of a spacelike Delaunay surface with conelike singular points consists of (2, 5)-cuspidal edges.
AB - Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular points on spacelike surfaces with non-zero constant mean curvature (spacelike CMC surfaces). We prove that spacelike CMC surfaces do not admit fold singular points. Moreover, we show that the singular point set of any conjugate CMC surface of a spacelike Delaunay surface with conelike singular points consists of (2, 5)-cuspidal edges.
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U2 - 10.14492/hokmj/1529308818
DO - 10.14492/hokmj/1529308818
M3 - Article
AN - SCOPUS:85048698244
SN - 0385-4035
VL - 47
SP - 245
EP - 267
JO - Hokkaido Mathematical Journal
JF - Hokkaido Mathematical Journal
IS - 2
ER -