Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592460 | Journal of Functional Analysis | 2007 | 18 Pages |
Abstract
We consider coefficient bodies Mn for univalent functions. Based on the Löwner–Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a representation of the Virasoro algebra. Then Mn are defined as sub-Riemannian manifolds. Given a Lie–Poisson bracket they form a grading of subspaces with the first subspace as a bracket-generating distribution of complex dimension two. With this sub-Riemannian structure we construct a new Hamiltonian system to calculate regular geodesics which turn to be horizontal. Lagrangian formulation is also given in the particular case M3.
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