The Kobayashi pseudometric for the Fock-Bargmann-Hartogs domain and its application (Q2303784)

Let \(D_{n,m}:=\{(z,w)\in\mathbb C^n\times\mathbb C^m: \|w\|^2<\exp(-\|z\|^2)\}\) be the Fock-Bargman-Hartogs domain. The authors present an effective description of all geodesics with respect to the Kobayashi-Royden pseudometric \(\mathcal K_{D_{n,1}}\). As a consequence, they get an effective formula for \(\mathcal K_{D_{n,1}}\). Finally, they establish a boundary version of the Schwarz lemma for mappings \(D_{1,1}\longrightarrow D_{n,m}\).