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On the holomorphic curvature of some intrinsic metrics


Author: B. Wong
Journal: Proc. Amer. Math. Soc. 65 (1977), 57-61
MSC: Primary 32H20
DOI: https://doi.org/10.1090/S0002-9939-1977-0454081-7
MathSciNet review: 0454081
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Abstract: If G is a hyperbolic manifold in the sense of Kobayashi and the differential Kobayashi metric $ {K_G}$ is of class $ {C^2}$, then the holomorphic curvature of $ {K_G}$ is greater than or equal to $ - 4$. If G is Carathéodory-hyperbolic and the differential Carathéodory metric $ {C_G}$ is of class $ {C^2}$, then the holomorphic curvature of $ {C_G}$ is less than or equal to $ - 4$. With this result we obtain an intrinsic characterization of the unit ball.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0454081-7
Keywords: Kobayashi metric, Carathéodory metric, holomorphic curvature
Article copyright: © Copyright 1977 American Mathematical Society

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