Timelike minimal surfaces via loop groups

J. Inoguchi, M. Toda

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28 Scopus citations


This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces. In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.

Original languageEnglish
Pages (from-to)313-355
Number of pages43
JournalActa Applicandae Mathematicae
Issue number3
StatePublished - Sep 2004


  • Harmonic maps
  • Loop groups
  • Lorentz surfaces
  • Timelike minimal surfaces


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