Invariant metrics on unbounded strongly pseudoconvex domains with non-compact automorphism group

摘要

We study invariant metrics on unbounded strongly pseudoconvex domains with non-compact automorphism group. The main result is that the corresponding Bergman and Khler-Einstein metrics are metrically equivalent. We also determine the comparisons among invariant metrics, including the Carath,odory and Kobayashi pseudo-metrics additionally.