Highly symmetric homogeneous Kobayashi-hyperbolic manifolds

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.