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The Kobayashi and Carathéodory pseudodistances for complex analytic manifolds. (English) Zbl 0806.32011

The author presents a discussion on the Carathéodory and Kobayashi pseudo-distances in the setting of complex analytic Banach manifolds over complex Banach spaces. The main known results on these two pseudo- distances in the classical setting of finite-dimensional complex analytic manifolds extend, in a natural way, to this analytic Banach manifolds setting. This extention is based on purely topological methods which are built in the very definition of these pseudo-distances. No discussion is given concerning the differential forms of these pseudo-distances.

MSC:

32K05 Banach analytic manifolds and spaces
32F45 Invariant metrics and pseudodistances in several complex variables
32Q99 Complex manifolds
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References:

[1] Chen, S. S., Carathéodory distances and convexity with respect to bounded holomorphic functions, (Proceedings of A.M.S., 39 (1973)), 305-307 · Zbl 0265.32012
[2] Kim, D. S., Carathéodory distance and bounded holomorphic functions, Duke Mathematical Journal, 41, 333-338 (1974) · Zbl 0287.32018
[3] Kobayashi, S., Hyperbolic Manifolds and Holomorphic Mappings (1970), Marcel Dekker: Marcel Dekker New York · Zbl 0207.37902
[4] Warner, W. F., Foundations of Differentiable Manifolds arid Lie Groups (1971), Scott and Foresman: Scott and Foresman Glenview, Illinois
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