

Complex analysis and mathematical physics
September 29, 2015 17:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)






EulerArnold equations in subRiemannian geometry on the
Teichmüller space and curve
A. Yu. Vasiliev^{} ^{} University of Bergen

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Abstract:
We consider the group of orientationpreserving
diffeomorphisms of the unit circle and its central extension, the
VirasoroBott group, with their respective horizontal distributions,
which are Ehresmann connections with respect to a projection to the
smooth universal Teichmüller space and the universal Teichmüller curve
associated to the space of normalized univalent functions. We find
equations for the normal subRiemannian geodesics with respect to the
pullback of the Kählerian metrics, namely, the VellingKirillov metric
on the class of normalized univalent functions and the WeilPetersson
metric on the universal Teichmüller space. The geodesic equations are
subRiemannian analogues of the EulerArnold equation and they lead to
the CLM, KdV and other known nonlinear PDEs.

