Hokkaido Mathematical Journal

The DPW method for constant mean curvature surfaces in 3-dimensional Lorentzian spaceforms, with applications to Smyth type surfaces

Yuta OGATA

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Abstract

We give criteria for singularities of spacelike constant mean curvature surfaces in 3-dimensional de Sitter and anti-de Sitter spaces constructed by the DPW method, which is a generalized Weierstrass representation. We also construct some examples of spacelike CMC surfaces, including analogs of Smyth surfaces with singularities, using appropriate models to visualize them.

Article information

Source
Hokkaido Math. J., Volume 46, Number 3 (2017), 315-350.

Dates
First available in Project Euclid: 7 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1510045301

Digital Object Identifier
doi:10.14492/hokmj/1510045301

Mathematical Reviews number (MathSciNet)
MR3720332

Zentralblatt MATH identifier
1379.53083

Subjects
Primary: 53B30: Lorentz metrics, indefinite metrics
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Keywords
differential geometry surface theory integrable systems

Citation

OGATA, Yuta. The DPW method for constant mean curvature surfaces in 3-dimensional Lorentzian spaceforms, with applications to Smyth type surfaces. Hokkaido Math. J. 46 (2017), no. 3, 315--350. doi:10.14492/hokmj/1510045301. https://projecteuclid.org/euclid.hokmj/1510045301


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