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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Classifying maps in fiberings of homogeneous bounded domains
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by Soji Kaneyuki PDF
Proc. Amer. Math. Soc. 52 (1975), 283-288 Request permission

Abstract:

A homogeneous bounded domain in ${{\text {C}}^n}$ admits a structure of a fiber space whose base and fibers are homogeneous bounded domains. For such a fibering there exists a universal fiber space with the same fibers, which plays an analogous role as a universal bundle does in topology. A sufficient condition is given in order that the canonical map of the base of the fibering into the classifying domain is injective. Some applications of it are also given.
References
  • Soji Kaneyuki, On the automorphism groups of homogeneuous bounded domains, J. Fac. Sci. Univ. Tokyo Sect. I 14 (1967), 89–130 (1967). MR 227472
  • Soji Kaneyuki, Homogeneous bounded domains and Siegel domains, Lecture Notes in Mathematics, Vol. 241, Springer-Verlag, Berlin-New York, 1971. MR 0338467
  • I. I. Pjateckiĭ-Šapiro, The geometry and classification of bounded homogeneous regions, Uspehi Mat. Nauk 20 (1965), no. 2 (122), 3–51 (Russian). MR 0196131
  • 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
  • —, Geometry of classical domains and theory of automorphic functions, Fizmatgiz, Moscow, 1961; French transl., Dunod, Paris, 1966. MR 25 #231; 33 #5949.
  • Tadashi Tsuji, On infinitesmal automorphisms and homogeneous Siegel domains over circular cones, Proc. Japan Acad. 49 (1973), 390–393. MR 374501
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 283-288
  • MSC: Primary 32M10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0404714-4
  • MathSciNet review: 0404714