Sub-Riemannian geometry of the coefficients of univalent functions

dc.creatorMarkina, Irina
dc.creatorProkhorov, Dmitri
dc.creatorVasil'ev, Alexander
dc.date2006-08-22
dc.date.accessioned2026-07-07T07:22:01Z
dc.date.available2026-07-07T07:22:01Z
dc.descriptionWe consider coefficient bodies $\mathcal M_n$ 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 $\mathcal M_n$ 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 and calculate regular geodesics which turn to be horizontal. Lagrangian formulation is also given in the particular case $\mathcal M_3$.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0608532
dc.identifierhttp://arxiv.org/abs/math/0608532
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115510
dc.subjectComplex Variables
dc.subjectDifferential Geometry
dc.subject30C50; 17B66; 53C17
dc.titleSub-Riemannian geometry of the coefficients of univalent functions
dc.typetext

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