Open Access
June 2018 Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space
Atsufumi HONDA, Miyuki KOISO, Kentaro SAJI
Hokkaido Math. J. 47(2): 245-267 (June 2018). DOI: 10.14492/hokmj/1529308818


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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Atsufumi HONDA. Miyuki KOISO. Kentaro SAJI. "Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space." Hokkaido Math. J. 47 (2) 245 - 267, June 2018.


Published: June 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06901705
MathSciNet: MR3815292
Digital Object Identifier: 10.14492/hokmj/1529308818

Primary: 53A10
Secondary: 53A35 , 53C50

Keywords: (2,5)-cuspidal edge , constant mean curvature , fold , Spacelike CMC surface

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

Vol.47 • No. 2 • June 2018
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