Compact Courses
Automorphism groups of Kobayashi-hyperbolic manifolds
by
Prof. Alexander V. Isaev
Australian National University, Australia
from
January 27 - 30 and February 02 - 03, 2009
at
10AM, L H – 1, Department of Mathematics
Indian Institute of Science, Bangalore
Abstract
I will give a reasonably detailed exposition of results describing Kobayashi-hyperbolic manifolds for which the dimension of the group of holomorphic automorphisms is "sufficiently high". The classification problem for hyperbolic manifolds with high-dimensional automorphism group can be thought of as a complex-geometric analogue of that for Riemannian manifolds with high-dimensional isometry group, which inspired many results in the 1950's-70's. Although the methods presented here are almost entirely different from those utilized in the Riemannian case, there is a common property that made these classifications possible: both the action of the holomorphic automorphism group of a hyperbolic manifold and the action of the isometry group of a Riemannian manifold are proper on the respective manifolds. The properness of the action will be central to our exposition.
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