A solvable string on a Lorentzian surface

Jeanne Clelland, Peter VASSILIOU

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    It is shown that there are nonlinear sigma models which are Darboux integrable and possess a solvable Vessiot group in addition to those whose Vessiot groups are central extensions of semi-simple Lie groups. They govern harmonic maps between Minkowski space R1,1 and certain complete, non-constant curvature 2-metrics. The solvability of the Vessiot group permits a reduction of the general Cauchy problem to quadrature. We treat the specific case of harmonic maps from Minkowski space into a non-constant curvature Lorentzian 2-metric, λ. Despite the completeness of λ we exhibit a Cauchy problem with real analytic initial data which blows up in finite time. We also derive a hyperbolic Weierstrass representation formula for all harmonic maps from R1,1 into λ.

    Original languageEnglish
    Pages (from-to)177-198
    Number of pages22
    JournalDifferential Geometry and Its Applications
    Volume33
    DOIs
    Publication statusPublished - Mar 2014

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