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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Holomorphic sectional curvature of quasisymmetric domains
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by R. Zelow PDF
Proc. Amer. Math. Soc. 76 (1979), 299-301 Request permission

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).
References
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  • Shingo Murakami, On automorphisms of Siegel domains, Lecture Notes in Mathematics, Vol. 286, Springer-Verlag, Berlin-New York, 1972. MR 0364690, DOI 10.1007/BFb0058567
  • I. I. Pyateskii-Shapiro, Automorphic functions and the geometry of classical domains, Mathematics and its Applications, Vol. 8, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Translated from the Russian. MR 0252690
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    • —, Forthcoming book about algebraic structures on symmetric domains (to appear).
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  • R. Zelow Lundquist, Curvature of quasisymmetric Siegel domains, J. Differential Geometry 14 (1979), no. 4, 629–655 (1981). MR 600619
  • Rune Zelow Lundquist, On the geometry of some Siegel domains, Nagoya Math. J. 73 (1979), 175–195. MR 524015, DOI 10.1017/S0027763000018390
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 76 (1979), 299-301
  • MSC: Primary 53C55; Secondary 32M10
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0537092-4
  • MathSciNet review: 537092