Advanced Studies in Pure Mathematics

Triply periodic zero mean curvature surfaces in Lorentz-Minkowski 3-space

Shoichi Fujimori

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We construct triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space $\mathbb{L}^3$, with the same topology as the triply periodic minimal surfaces in the Euclidean 3-space $\mathbb{R}^3$, called Schwarz rPD surfaces.

Article information

Singularities in Generic Geometry, S. Izumiya, G. Ishikawa, M. Yamamoto, K. Saji, T. Yamamoto and M. Takahashi, eds. (Tokyo: Mathematical Society of Japan, 2018), 201-219

Received: 7 July 2016
Revised: 8 March 2017
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538618974

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

zero mean curvature triply periodic surface fold singularity


Fujimori, Shoichi. Triply periodic zero mean curvature surfaces in Lorentz-Minkowski 3-space. Singularities in Generic Geometry, 201--219, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07810201.

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