Vasil'ev A. Sub-Riemannian geodesic equations on the Virasoro-Bott group, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)
Speaker: Alexander Vasil'ev
Title: Sub-Riemannian geodesic equations on the Virasoro-Bott group
Abstract:
The Virasoro-Bott group is an essentially unique central extension for the group of orientation-preserving diffeomorphisms of the unit circle. The horizontal distributions on this group is naturally chosen with respect to projections to the smooth universal Teichmüller space and the universal Teichmüller curve. These distributions correspond to factorization with respect to subgroups of rotations and the conformal subgroup respectively. We study geodesics on the Virasoro-Bott group with respect to biinvariant constant type metrics on distributions. The geodesic equations on the Virasoro algebra are sub-Riemannian analogues of the Euler-Arnold hydrodynamic equations.