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