Timelike Minimal Surfaces via Loop Groups

2004/09/05 by Jun-ichi Inoguchi, Magdalena Toda · 1 citation
Mathematics · #math.DG #msc:53A10 #msc:58E20 #msc:22E67

paper · pdf

published as Acta Applicandae Mathematicae, vol. 83, no. 3, (II), 2004, pp 313-355 · 43 pages, 3 figures

arxiv created 2004/09/05 · arxiv updated 2009/12/01

Abstract

We study manifolds with split-complex structure and apply some general results to the study of Lorentz surfaces. In particular, we apply our results to timelike minimal immersions. The conformal realization of these surfaces is obtained using a representation based on loop groups. The classical Weierstrass representation (integral formula) is recovered as a byproduct of this general setting.

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• Timelike minimal surface in 𝔼³₁ with arbitrary ends

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