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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Inequalities between intrinsic metrics


Author: Jacob Burbea
Journal: Proc. Amer. Math. Soc. 67 (1977), 50-54
MSC: Primary 32H15
DOI: https://doi.org/10.1090/S0002-9939-1977-0481121-1
MathSciNet review: 0481121
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Abstract: We introduce the ``mth order Carathéodory-Reiffen metric,'' the ``mth order Bergman metric'' and the ``mth order modified Bergman metric'' on M. Here M is a complex manifold which is ample in a suitable sense. These ``metrics'' are defined on $ T(M)$ and they are intrinsic. They arise as solutions of maximum problems. The first orders of these ``metrics'' (except for the modified Bergman metric) are the corresponding familiar metrics. All these metrics are biholomorphically invariant. We establish a chain of inequalities between them. This generalizes an earlier result of Hahn, proved by different methods.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0481121-1
Keywords: Bergman metric, Carathéodory-Reiffen metric
Article copyright: © Copyright 1977 American Mathematical Society