Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

A note on the Kobayashi-Royden metric for real ellipsoids

Author(s): Wlodzimierz Zwonek
Journal: Proc. Amer. Math. Soc. 125 (1997), 199-202.
MSC (1991): Primary 32H15
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

[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


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS