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A note on the Kobayashi-Royden metric
for real ellipsoids

Author: Wlodzimierz Zwonek
Journal: Proc. Amer. Math. Soc. 125 (1997), 199-202
MSC (1991): Primary 32H15
MathSciNet review: 1353411
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Abstract: We give a proof of the fact proven by L.D. Kay that the Kobayashi-Royden metric of a real ellipsoid (of dimension at least $2$) at $0$ is hermitian exactly when the ellipsoid is the ball. The proof given by us is much simpler and shorter than that of Kay although it is based on the same results.

References [Enhancements On Off] (What's this?)

  • [Gen] G. Gentili, Regular complex geodesics in the domain $D_{n}=\{(z_{1},\ldots ,z_{n})\in \mathbb {C}^{n}:|z_{1}|+\ldots +|z_{n}|<1\}$, in: Lecture Notes in Math. 1277, Springer, (1987), 35-45. MR 89f:32044
  • [Jar-Pfl] M. Jarnicki, P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993. MR 94k:32039
  • [Kay] L. D. Kay, On the Kobayashi-Royden metric for ellipsoids, Math. Ann. 289 (1991), 55-72. MR 92a:32030
  • [Lem] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. Fr. 109 (1981), 427-474. MR 84d:32036

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Wlodzimierz Zwonek
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland

Received by editor(s): July 21, 1995
Additional Notes: This paper has been supported by KBN grant No 2 PO3A 060 08.
Communicated by: Eric Bedford
Article copyright: © Copyright 1997 American Mathematical Society

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