Advanced Studies in Pure Mathematics

Weierstrass-type representations for timelike surfaces

Masashi Yasumoto

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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

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

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

Permanent link to this document euclid.aspm/1538618986

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: 52C99: None of the above, but in this section


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.

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