Sub-Riemannian geometry of the coefficients of univalent functions
| dc.creator | Markina, Irina | |
| dc.creator | Prokhorov, Dmitri | |
| dc.creator | Vasil'ev, Alexander | |
| dc.date | 2006-08-22 | |
| dc.date.accessioned | 2026-07-07T07:22:01Z | |
| dc.date.available | 2026-07-07T07:22:01Z | |
| dc.description | We 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.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608532 | |
| dc.identifier | http://arxiv.org/abs/math/0608532 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115510 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 30C50; 17B66; 53C17 | |
| dc.title | Sub-Riemannian geometry of the coefficients of univalent functions | |
| dc.type | text |