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On holomorphic isometries for the Kobayashi and Carathéodory distances on complex manifolds. (English) Zbl 0741.32018
The author gives characterization of biholomorphic mappings from convex bounded domains to complete circular domains in terms of local isometry properties of these mappings in Kobayashi and Carathéodory pseudodistances.

##### MSC:
 32F45 Invariant metrics and pseudodistances in several complex variables 32A07 Special domains in $${\mathbb C}^n$$ (Reinhardt, Hartogs, circular, tube) (MSC2010)