Cornelia Vizman
Generalized Euler-Poincar\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications.
Fri, 08/27/2010 - 15:01 — SomNambulAuthors: Cornelia Vizman, Feride Tiglay
Subjects: Analysis of PDEs
AbstractWe 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 geodesiAbelian extensions via prequantization.
Wed, 10/21/2009 - 14:15 — SomNambulAuthors: Cornelia Vizman
Subjects: Differential Geometry
AbstractWe 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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