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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Revêtements et isométries pour la métrique infinitésimale de Kobayashi
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by Jean-Pierre Vigué PDF
Proc. Amer. Math. Soc. 129 (2001), 3279-3284 Request permission

Abstract:

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
  • Email: vigue@mathlabo.univ-poitiers.fr
  • Received by editor(s): March 10, 2000
  • Published electronically: March 29, 2001
  • Communicated by: Steven R. Bell
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3279-3284
  • MSC (2000): Primary 32F45
  • DOI: https://doi.org/10.1090/S0002-9939-01-05977-9
  • MathSciNet review: 1845003