Hokkaido Mathematical Journal

Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space

Atsufumi HONDA, Miyuki KOISO, and Kentaro SAJI

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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.

Article information

Hokkaido Math. J., Volume 47, Number 2 (2018), 245-267.

First available in Project Euclid: 18 June 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53A35: Non-Euclidean differential geometry 53C50: Lorentz manifolds, manifolds with indefinite metrics

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


HONDA, Atsufumi; KOISO, Miyuki; SAJI, Kentaro. Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space. Hokkaido Math. J. 47 (2018), no. 2, 245--267. doi:10.14492/hokmj/1529308818. https://projecteuclid.org/euclid.hokmj/1529308818

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