The Gauss map for nearly-Fuchsian manifolds

Abstract: In this talk we will study the Gauss map for nearly-Fuchsian manifolds, namely complete hyperbolic n-manifolds homeomorphic to HxR, where H is a closed hypersurface with principal curvatures smaller than one in absolute value. The Gauss map of such a hypersurface is a Lagrangian equivariant embedding in the space of oriented geodesics of hyperbolic space, which is known to have a natural para-Kähler structure. We will present two characterizations of the Lagrangian equivariant embeddings obtained in this way, the first in terms of the vanishing of the Maslov class, and the second in terms of orbits of the group of Hamiltonian symplectomorphisms.

This is joint work with Christian El Emam (Pavia).

differential geometry

Audience: researchers in the topic

Pangolin seminar

Series comments: TIME HAS CHANGED: 15:30 Paris 10:30AM Rio de Janeiro

Description: Differential geometry seminar

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