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On the geometry of some Siegel domains

Published online by Cambridge University Press:  22 January 2016

Rune Zelow
Rune Zelow*
Affiliation:
Univ. of Calif., Berkeley
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In his book [2], Pyatetskii-Shapiro describes representations of classical domains as certain “fibrations” over their boundary components. The fibers are quasi-symmetric Siegel domains of the second kind [3]. Professor Kobayashi asked “how symmetric” these fibers are, or more precisely, he asked for totally geodesic directions in the fiber. The object of this paper is to determine at least a totally geodesic sub-manifold of the fiber, and it turns out to be complex.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 73 , March 1979 , pp. 175 - 195
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[1] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, vol. II, Interscience Tracts #15, Interscience, New York, 1969.Google Scholar
[2] Pyatetskii-Shapiro, I. I., Automorphic Functions and the Geometry of Classical Domains, Gordon and Breach, New York, 1969.Google Scholar
[3] Satake, I., On classification of quasi-symmetric domains, Nagoya Math. J. 62 (1976), pp. 1–12.Google Scholar
[4] Zelow (Lundquist), R., On the geometry of quasi-symmetric domains, (to appear).Google Scholar