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Proceedings of the American Mathematical Society

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



Classifying maps in fiberings of homogeneous bounded domains

Author: Soji Kaneyuki
Journal: Proc. Amer. Math. Soc. 52 (1975), 283-288
MSC: Primary 32M10
MathSciNet review: 0404714
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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 [Enhancements On Off] (What's this?)

  • [1] S. Kaneyuki, On the automorphism groups of homogeneous bounded domains, J. Fac. Sci. Univ. Tokyo Sect. I 14 (1967), 89-130. MR 37 #3056. MR 0227472 (37:3056)
  • [2] -, Homogeneous bounded domains and Siegel domains, Lecture Notes in Math., vol. 241, Springer-Verlag, Berlin, 1971. MR 0338467 (49:3231)
  • [3] I. I. Pjateckiĭ-Šapiro, The geometry and classification of bounded homogeneous regions, Uspehi Mat. Nauk 20 (1965), no. 2 (122), 3-51 = Russian Math. Surveys 20 (1965), no. 2, 1-48. MR 33 #4323. MR 0196131 (33:4323)
  • [4] -, Automorphic functions and the geometry of classical domains, Fizmatgiz, Moscow, 1961; English transl., Math. and its Applications, vol. 8, Gordon and Breach, New York, 1969. MR 25 #231; 40 #5908. MR 0252690 (40:5908)
  • [5] -, Geometry of classical domains and theory of automorphic functions, Fizmatgiz, Moscow, 1961; French transl., Dunod, Paris, 1966. MR 25 #231; 33 #5949.
  • [6] T. Tsuji, On infinitesimal automorphisms and homogeneous Siegel domains over circular cones, Proc. Japan Acad. 49 (1973), 390-393. MR 0374501 (51:10701)

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Keywords: Homogeneous bounded domains, bounded symmetric domains, $ j$-algebras
Article copyright: © Copyright 1975 American Mathematical Society

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