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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Holomorphic sectional curvature of quasisymmetric domains


Author: R. Zelow
Journal: Proc. Amer. Math. Soc. 76 (1979), 299-301
MSC: Primary 53C55; Secondary 32M10
MathSciNet review: 537092
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Abstract: It is well known that the holomorphic sectional curvature of a bounded symmetric domain is bounded above by a negative constant. In this paper we show that this is true more generally for a quasi-symmetric Siegel domain, and the proof is based on a formula for the curvature from the author's thesis. The bounded homogeneous domains are, as is well known, biholomorphic to homogeneous Siegel domains and the bounded symmetric domains are biholomorphic to those quasi-symmetric (homogeneous) Siegel domains that satisfy a certain algebraic identity (which we do not need here).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0537092-4
PII: S 0002-9939(1979)0537092-4
Keywords: Bounded homogeneous domain, bounded symmetric domain, Bergman metric, quasi-symmetric Siegel domain, cone, tube domain
Article copyright: © Copyright 1979 American Mathematical Society