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Cornelia Vizman

  1. Generalized Euler-Poincar\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications.

    Пт, 08/27/2010 - 15:01 — SomNambul
    Authors: Cornelia Vizman, Feride Tiglay
    Subjects: Analysis of PDEs
    Abstract

    We develop the necessary tools, including a notion of logarithmic derivative
    for curves in homogeneous spaces, for deriving a general class of equations
    including Euler-Poincar\'e equations on Lie groups and homogeneous spaces.
    Orbit invariants play an important role in this context and we use these
    invariants to prove global existence and uniqueness results for a class of PDE.
    This class includes Euler-Poincar\'e equations that have not yet been
    considered in the literature as well as integrable equations like Camassa-Holm,
    Degasperis-Procesi, $\mu$CH and $\mu$DP equations, and the geodesi

  2. Abelian extensions via prequantization.

    Ср, 10/21/2009 - 14:15 — SomNambul
    Authors: Cornelia Vizman
    Subjects: Differential Geometry
    Abstract

    We generalize the prequantization central extension of a group of
    diffeomorphisms preserving a closed 2--form $\omega$ ($\omega$--invariant
    diffeomorphisms) to an abelian extension of a group of diffeomorphisms
    preserving a closed vector valued 2--form $\omega$ up to a linear isomorphism
    ($\omega$--equivariant diffeomorphisms). Every abelian extension of a simply
    connected Lie group can be obtained as the pull-back of such a prequantization
    abelian extension.

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