Complex geodesics and holomorphic retracts of dimension 1
Let \(D\) be a bounded domain in \(\mathbb{C}^n\) and \(V\) an analytic subvariety of \(D\). In the case where \(V\) is biholomorphically equivalent to the unit disc in \(\mathbb{C}\), \textit{L. Lempert} gave a characterization of complex geodesics by holomorphic retraction [Anal. Math. 8, 257-261 (1982; Zbl 0509.32015)]. After the study of Lempert, the author deals with the case where \(V\) is a hyperbolic subvariety of dimension 1. To this end, he defines new invariant metrics, one is of Carathéodory type and another one is of Kobayashi type. He proves two fundamental results similar to the theorem of Lempert. He gives calculations of the above pseudometrics in a certain simple case and its application.
scientific article; zbMATH DE number 1472033
scientific article