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The Bergman metric on a Stein manifold with a bounded plurisubharmonic function
Author(s):
Bo-Yong
Chen;
Jin-Hao
Zhang
Journal:
Trans. Amer. Math. Soc.
354
(2002),
2997-3009.
MSC (2000):
Primary 32H10
Posted:
March 29, 2002
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Abstract:
In this article, we use the pluricomplex Green function to give a sufficient condition for the existence and the completeness of the Bergman metric. As a consequence, we proved that a simply connected complete Kähler manifold possesses a complete Bergman metric provided that the Riemann sectional curvature  , which implies a conjecture of Greene and Wu. Moreover, we obtain a sharp estimate for the Bergman distance on such manifolds.
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Additional Information:
Bo-Yong
Chen
Affiliation:
Department of Applied Mathematics, Tongji University, Shanghai 200092, China
Email:
chenboy@online.sh.cn
Jin-Hao
Zhang
Affiliation:
Department of Mathematics, Fudan University, Shanghai 200433, China
Email:
zhangjhk@online.sh.cn
DOI:
10.1090/S0002-9947-02-02989-6
PII:
S 0002-9947(02)02989-6
Keywords:
Bergman metric,
pluricomplex Green function,
sectional curvature,
K\"ahler manifold
Received by editor(s):
August 1, 2001
Posted:
March 29, 2002
Additional Notes:
The first author was supported by an NSF grant TY10126005 and a grant from Tongji Univ. No. 1390104014
The second author was supported by project G1998030600
Copyright of article:
Copyright
2002,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Bo-Yong Chen and Jin-Hao Zhang, The Bergman metric on a Stein manifold with a bounded plurisubharmonic function, Transactions of the American Mathematical Society 354 (2002), 2997-3009.
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