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Revêtements et isométries pour la métrique infinitésimale de Kobayashi

Author: Jean-Pierre Vigué
Journal: Proc. Amer. Math. Soc. 129 (2001), 3279-3284
MSC (2000): Primary 32F45
Published electronically: March 29, 2001
MathSciNet review: 1845003
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In this paper, we prove that, under some hypothesis on the domains, if a holomorphic mapping $ f:D_{1}\longrightarrow D_{2}$ is an isometry for the Kobayashi infinitesimal metric at a point, it is a covering map. In the case $ D_{1} = D_{2}$, we prove, in certain cases, that $f$ is an analytic isomorphism.

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Additional Information

Jean-Pierre Vigué
Affiliation: UPRES A 6086 Groupes de Lie et Géométrie, SP2MI, Mathématiques, Université de Poitiers, BP 30179, 86962 Futuroscope Cedex, France

Received by editor(s): March 10, 2000
Published electronically: March 29, 2001
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society

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