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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
DOI: https://doi.org/10.1090/S0002-9939-01-05977-9
Published electronically: March 29, 2001
MathSciNet review: 1845003
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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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  • [1] L. Belkhchicha. Caractérisation des isomorphismes analytiques sur la boule-unité de ${\mathbb{ C}}^{n} $ pour une norme. Math. Z. 215 (1994), p. 129-141. MR 94m:32037
  • [2] H. Cartan. Sur les fonctions de plusieurs variables complexes. L'itération des transformations intérieures d'un domaine borné. Math. Z. 35 (1932), p. 760-773.
  • [3] T. Franzoni and E. Vesentini. Holomorphic maps and invariant distances. Math. Studies 40, North-Holland, Amsterdam, 1980. MR 82a:32032
  • [4] I. Graham. Holomorphic mappings into strictly convex domains which are Kobayashi isometries at a point. Proc. Amer. Math. Soc. 105 (1989), p. 917- 921. MR 89k:32048
  • [5] M. Greenberg. Lectures on algebraic topology. W. A. Benjamin, New-York, (1967). MR 35:6137
  • [6] M. Jarnicki and P. Pflug. Invariant distances and metrics in complex analysis. De Gruyter Expositions in Mathematics 9, De Gruyter, Berlin, 1993. MR 94k:32039
  • [7] S. Kobayashi. Intrinsic distances, measures and geometric function theory. Bull. Amer. Math. Soc. 82 (1976), p. 357-416. MR 54:3032
  • [8] L. Lempert. Holomorphic retracts and intrinsic metrics in convex domains. Anal. Math., 8 (1982), p. 257-261. MR 84f:32026
  • [9] H. Royden and P. Wong. Carathéodory and Kobayashi metrics on convex domains. Preprint (1983).
  • [10] E. Spanier. Algebraic topology. McGraw-Hill, New York 1966. MR 35:1007
  • [11] J.-P. Vigué. Caractérisation des automorphismes analytiques d'un domaine convexe borné. C. R. Acad. Sc. Paris Série I Math., 299 (1984), p. 101-104. MR 85h:32042
  • [12] J.-P. Vigué. Sur la caractérisation des automorphismes analytiques d'un domaine borné. Portugaliae Math. 43 (1986), p. 439-453. MR 89a:32029
  • [13] H. Wu. Normal families of holomorphic mappings. Acta Math. 119 (1967), p. 194-233. MR 37:468

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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

DOI: https://doi.org/10.1090/S0002-9939-01-05977-9
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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