Holomorphic sectional curvature of quasisymmetric domains

Author:
R. Zelow

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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).

**[1]**S. Kaneyuki,*On the automorphism groups of homogeneous bounded domains*, J. Fac. Sci. Univ. Tokyo**14**(1967), 87-130. MR**0227472 (37:3056)****[2]**S. Murakami,*On automorphisms of Siegel domains*, Lecture Notes in Math., vol. 286, Springer-Verlag, Berlin and New York, 1972. MR**0364690 (51:944)****[3]**I. I. Pjateckiĭ-Sapiro,*Automorphic functions and the geometry of classical domains*, Gordon and Breach, New York, 1969. MR**0252690 (40:5908)****[4]**I. Satake,*On the classification of quasi-symmetric domains*, Nagoya Math. J.**62**(1976), 1-12. MR**0412491 (54:614)****[5]**-, Forthcoming book about algebraic structures on symmetric domains (to appear).**[6]**M. Takeuchi,*Homogeneous Siegel domains*, Publications of the Study Group of Geometry, vol. 7, Institute of Mathematics, Yoshida College, Kyoto Univ., Kyoto, 1973. MR**0407332 (53:11108)****[7]**R. Zelow (Lundquist),*Curvature of quasi-symmetric domains*, J. Differential Geometry (to appear). MR**600619 (82c:32035)****[8]**-,*On the geometry of some Siegel domains*, Nagoya Math. J.**73**(1979), 175-195. MR**524015 (80m:32033)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
53C55,
32M10

Retrieve articles in all journals with MSC: 53C55, 32M10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0537092-4

Keywords:
Bounded homogeneous domain,
bounded symmetric domain,
Bergman metric,
quasi-symmetric Siegel domain,
cone,
tube domain

Article copyright:
© Copyright 1979
American Mathematical Society