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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Analysis of the Wu metric. I: The case of convex Thullen domains


Authors: C. K. Cheung and Kang-Tae Kim
Journal: Trans. Amer. Math. Soc. 348 (1996), 1429-1457
MSC (1991): Primary 32H20
DOI: https://doi.org/10.1090/S0002-9947-96-01642-X
MathSciNet review: 1357392
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Abstract: We present an explicit description of the Wu metric on the convex Thullen domains which turns out to be the first natural example of a purely Hermitian, non-Kählerian invariant metric. Also, we show that the Wu metric on these Thullen domains is in fact real analytic everywhere except along a lower dimensional subvariety, and is $C^{1}$ smooth overall. Finally, we show that the holomorphic curvature of the Wu metric on these Thullen domains is strictly negative where the Wu metric is real analytic, and is strictly negative everywhere in the sense of current.


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Additional Information

C. K. Cheung
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02167
Email: cheung/mt@hermes.bc.edu

Kang-Tae Kim
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784 South Korea
Email: kimkt@posmath.postech.ac.kr

DOI: https://doi.org/10.1090/S0002-9947-96-01642-X
Keywords: Kobayashi metric, invariant Hermitian metric, hyperbolic complex manifold, smoothness, holomorphic curvature
Received by editor(s): February 6, 1995
Additional Notes: Research of the second named author is supported in part by grants from Pohang University of Science and Technology and GARC of Seoul National University.
Article copyright: © Copyright 1996 American Mathematical Society