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2008 - 2009
announces
compact course on
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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