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Marginally trapped surfaces in L4 and an extended Weierstrass-Bryant representation

Juan A. Aledo·Jose A. Galvez·Pablo Mira
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Abstract

We give a conformal representation in terms of meromorphic data for a certain class of spacelike surfaces in the Lorentz-Minkowski 4-space L^4 whose mean curvature vector is either lightlike or zero at each point. This representation extends simultaneously the Weierstrass representation for minimal surfaces in Euclidean 3-space and for maximal surfaces in the Lorentz-Minkowski 3-space, and the Bryant representation for mean curvature one surfaces in the hyperbolic 3-space and in the de Sitter 3-space.

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Juan A. Aledo, Jose A. Galvez, Pablo Mira. 2005-03-30. Marginally trapped surfaces in L4 and an extended Weierstrass-Bryant representation. https://arxiv.org/abs/math/0503702

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