Some counterexamples concerning intrinsic distances

Author:

Barth Theodore J.

Abstract

Examples of the following are given: (i) complex spaces whose Carathéodory distances are not inner; (ii) a taut complex space that is not complete hyperbolic; (iii) a complex space that is complete hyperbolic mod Δ \bmod \; \Delta but not taut mod Δ \bmod \; \Delta ; (iv) a bounded pseudoconvex domain that is not taut.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

1. The Kobayashi distance induces the standard topology;Barth, Theodore J.;Proc. Amer. Math. Soc.,1972

2. N. Kerzman, Taut manifolds and domains of holomorphy in 𝐂ⁿ, Notices Amer. Math. Soc. 16 (1969), 675-676. Abstract #69T-B120.

3. On the relations between taut, tight and hyperbolic manifolds;Kiernan, Peter;Bull. Amer. Math. Soc.,1970

4. Holomorphic mappings into projective space with lacunary hyperplanes;Kobayashi, Shoshichi;Nagoya Math. J.,1973

5. Invariant distances on complex manifolds and holomorphic mappings;Kobayashi, Shoshichi;J. Math. Soc. Japan,1967

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5. The simplest example for the non-innerness of the Carathéodory distance Marek Jarnicki and Peter Pflug;Results in Mathematics;1990-08

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