Timelike minimal surfaces via loop groups

J. Inoguchi, M. Toda

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

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
Volume83
Issue number3
DOIs
StatePublished - Sep 2004

Keywords

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

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