Advanced Studies in Pure Mathematics

Weierstrass-type representations for timelike surfaces

Masashi Yasumoto

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Abstract

In this paper we give the Weierstrass-type representation for Lorentz conformal minimal surfaces in Minkowski 3-space that was derived by Konderak, and a new one for Lorentz conformal constant mean curvature 1 surfaces in anti de Sitter 3-space, using integrable systems techniques. As an application, we analyze their singularities. Finally, we describe first steps toward discretization of these timelike surfaces.

Article information

Source
Singularities in Generic Geometry, S. Izumiya, G. Ishikawa, M. Yamamoto, K. Saji, T. Yamamoto and M. Takahashi, eds. (Tokyo: Mathematical Society of Japan, 2018), 449-469

Dates
Received: 1 April 2016
Revised: 28 April 2017
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538618986

Digital Object Identifier
doi:10.2969/aspm/07810449

Mathematical Reviews number (MathSciNet)
MR3839958

Zentralblatt MATH identifier
07085116

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 52C99: None of the above, but in this section

Citation

Yasumoto, Masashi. Weierstrass-type representations for timelike surfaces. Singularities in Generic Geometry, 449--469, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07810449. https://projecteuclid.org/euclid.aspm/1538618986


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