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Analysis of the Wu metric II:
The case of non-convex Thullen domains

Authors: C. K. Cheung and K. T. Kim
Journal: Proc. Amer. Math. Soc. 125 (1997), 1131-1142
MSC (1991): Primary 32H15
MathSciNet review: 1363414
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Abstract: We present an explicit description of the Wu invariant metric on the non-convex Thullen domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys better regularity in this case. Furthermore, we show that the holomorphic curvature of the Wu metric is bounded from above everywhere by $-1/2$. This leads the Wu metric to be a natural solution to a conjecture of Kobayashi in the case of non-convex Thullen domains.

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Additional Information

C. K. Cheung
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02167
Email: Cheung/

K. T. Kim
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784 Republic of Korea

Keywords: Kobayashi metric, invariant Hermitian metric, hyperbolic complex manifold, smoothness, holomorphic curvature, Thullen domain
Received by editor(s): October 11, 1995
Additional Notes: Research of the second named author is supported in part by Grants from Pohang University of Science and Technology (POSTECH), GARC, and BSRI
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society