Pluriharmonic maps into Kähler symmetric spaces and Sym’s formula View Full Text


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Article Info

DATE

2009-01-15

AUTHORS

J.-H. Eschenburg, P. Quast

ABSTRACT

A construction due to Sym and Bobenko recovers constant mean curvature surfaces in euclidean 3-space from their harmonic Gauss maps. We generalize this construction to higher dimensions and codimensions replacing the surface by a complex manifold and the sphere (the target space of the Gauss map) by a Kähler symmetric space of compact type with its standard embedding into the Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{g}}$$\end{document} of its transvection group. Thus we obtain a new class of immersed Kähler submanifolds of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{g}}$$\end{document} and we derive their properties. More... »

PAGES

469

References to SciGraph publications

  • 2003-11. Pluriharmonic Maps, Loop Groups and Twistor Theory in ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
  • 1984. Noether’s Theorem for Harmonic Maps in DIFFERENTIAL GEOMETRIC METHODS IN MATHEMATICAL PHYSICS
  • 1980-02. Symmetric submanifolds of euclidean space in MATHEMATISCHE ANNALEN
  • 1985. Soliton surfaces and their applications (soliton geometry from spectral problems) in GEOMETRIC ASPECTS OF THE EINSTEIN EQUATIONS AND INTEGRABLE SYSTEMS
  • 1998-12. Associated families of pluriharmonic maps and isotropy in MANUSCRIPTA MATHEMATICA
  • 2007-01-06. Pluriharmonic maps of maximal rank in MATHEMATISCHE ZEITSCHRIFT
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    http://dx.doi.org/10.1007/s00209-008-0472-9

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