Hokkaido Mathematical Journal

Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space

Atsufumi HONDA, Miyuki KOISO, and Kentaro SAJI

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Abstract

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

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

Dates
First available in Project Euclid: 18 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1529308818

Digital Object Identifier
doi:10.14492/hokmj/1529308818

Mathematical Reviews number (MathSciNet)
MR3815292

Zentralblatt MATH identifier
06901705

Subjects
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

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

Citation

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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