A solvable string on a Lorentzian surface

Jeanne Clelland, Peter VASSILIOU

    Research output: Contribution to journalArticle

    2 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

    Fingerprint

    Harmonic Maps
    Strings
    Minkowski Space
    Cauchy Problem
    Curvature
    Weierstrass Representation
    Metric
    Lie groups
    Nonlinear sigma Model
    Central Extension
    Semisimple Lie Group
    Representation Formula
    Solvable Group
    Quadrature
    Blow-up
    Solvability
    Completeness

    Cite this

    Clelland, Jeanne ; VASSILIOU, Peter. / A solvable string on a Lorentzian surface. In: Differential Geometry and Its Applications. 2014 ; Vol. 33. pp. 177-198.
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    A solvable string on a Lorentzian surface. / Clelland, Jeanne; VASSILIOU, Peter.

    In: Differential Geometry and Its Applications, Vol. 33, 03.2014, p. 177-198.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A solvable string on a Lorentzian surface

    AU - Clelland, Jeanne

    AU - VASSILIOU, Peter

    PY - 2014/3

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    KW - Cauchy problem

    KW - Darboux integrability

    KW - Harmonic map

    KW - Pseudo-Riemannian surface

    KW - Weierstrass representation

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    JF - Differential Geometry and Its Applications

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