Invariant metrics and complex geodesics in several complex variables -

Abstract

Biholomorhically invariant metrics are important tools in Several Complex Variables which generalize Hermitian metrics and are particularly adapted for the study of holomorphic maps and function spaces. The Carath́eodory metric and the Kobayashi metric are instances of such metrics. The main goal of this thesis is to study the elementary properties of geodesics related to these two metrics.