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A Note on the Bergman metric of Bounded homogeneous Domains

Published online by Cambridge University Press:  11 January 2016

Chifune Kai  and
Takeo Ohsawa
Chifune Kai
Affiliation:
Faculty of Mathematics Kyushu University Higashi-ku 812-8581, Fukuoka Japan kai@math.kyushu-u.ac.jp
Takeo Ohsawa
Affiliation:
Graduate School of Mathematics Nagoya University Chikusa-ku 464-8602, Nagoya Japan ohsawa@math.nagoya-u.ac.jp
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Abstract

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We show that the Bergman metric of a bounded homogeneous domain has a potential function whose gradient has a constant norm with respect to the Bergman metric, and further that this constant is independent of the choice of such a potential function.

Keywords

32M10

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 186 , 2007 , pp. 157 - 163
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[1] Blocki, Z. and Pflug, P., Hyperconvexity and Bergman completeness, Nagoya Math. J., 151 (1998), 221–225.Google Scholar
[2] Carlehed, M., Cegrell, U. and Wikström, F., Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function, Ann. Polon. Math., 71 (1999), 87–103.CrossRefGoogle Scholar
[3] Chen, B.-Y., Bergman completeness of hyperconvex manifolds, Nagoya Math. J., 175 (2004), 165–170.CrossRefGoogle Scholar
[4] Chen, B.-Y., Infinite dimensionality of the middle L2-cohomology on non-compact Kähler hyperbolic manifolds, Publ. RIMS., 42 (2006), 683–689.Google Scholar
[5] Donnelly, H., L2 cohomology of the Bergman metric for weakly pseudoconvex domains, Illinois J. Math., 41 (1997), 151–160.Google Scholar
[6] Donnelly, H. and Fefferman, C., L 2-cohomology and index theorem for the Bergman metric, Ann. Math., 118 (1983), 593–618.Google Scholar
[7] Gromov, M., Kähler hyperbolicity and L2-Hodge theory, J. Diff. G., 33 (1991), 263–292.Google Scholar
[8] Herbort, G., The Bergman metric on hyperconvex domains, Math. Z., 232 (1999), 183–196.Google Scholar
[9] Ishi, H., On the Bergman metric of Siegel domains, preprint.Google Scholar
[10] Kobayashi, S., Hyperbolic Complex Spaces, Grundlehren der Math. Wiss. 318, Springer-Verlag, Berlin-Heidelberg-New York, 1998.Google Scholar
[11] Kobayashi, S., Hyperbolic Manifolds and Holomorphic Mappings (2nd edition) An Intro duction, World Sci., 2005.Google Scholar
[12] Nakajima, K., Some studies on Siegel domains, J. Math. Soc. Japan, 27 (1975), 54–75.Google Scholar
[13] Vinberg, É. B., Gindikin, S. G. and Pjateckiĭ-Sapiro, I. I., Classification and canonical realization of complex homogeneous bounded domains, Trudy Moskov. Mat. Obsc., 12 (1963), 359–388; Trans. Moscow Math. Soc, 12 (1963), 404–437.Google Scholar