Highly symmetric homogeneous Kobayashi-hyperbolic manifolds
Date
2021
Authors
Herrington, Elliot Michael
Editors
Advisors
Larusson, Finnur
Leistner, Thomas
Leistner, Thomas
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Thesis
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Abstract
Kobayashi-hyperbolic manifolds are an important and well-studied class of
complex manifolds defined by the property that the Kobayashi pseudodistance
is a true distance. Such manifolds that have automorphism group of
sufficiently high dimension can be classified up to biholomorphism, and the
goal of this thesis is to continue the classification of homogeneous Kobayashihyperbolic
manifolds started by Alexander Isaev in the early 2000s. We settle
the classification of such manifolds with automorphism group dimensions
n2 − 7 and n2 − 8, where n is the dimension of the manifold. We do so
by analysing the Lie algebra of the automorphism group of a Siegel domain
of the second kind corresponding to a homogeneous Kobayashi-hyperbolic
manifold of a given automorphism group dimension.
School/Discipline
School of Mathematical Sciences
Dissertation Note
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2021
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