A note on the Kobayashi-Royden metric for real ellipsoids
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- by Wlodzimierz Zwonek PDF
- Proc. Amer. Math. Soc. 125 (1997), 199-202 Request permission
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
- Graziano Gentili, Regular complex geodesics for the domain $D_n=\{(z_1,\cdots ,z_n)\in \textbf {C}^n\colon \;|z_1|+\cdots +|z_n|<1\}$, Complex analysis, III (College Park, Md., 1985–86) Lecture Notes in Math., vol. 1277, Springer, Berlin, 1987, pp. 35–45. MR 922333, DOI 10.1007/BFb0078244
- Marek Jarnicki and Peter Pflug, Invariant distances and metrics in complex analysis, De Gruyter Expositions in Mathematics, vol. 9, Walter de Gruyter & Co., Berlin, 1993. MR 1242120, DOI 10.1515/9783110870312
- L. D. Kay, On the Kobayashi-Royden metric for ellipsoids, Math. Ann. 289 (1991), no. 1, 55–72. MR 1087235, DOI 10.1007/BF01446557
- László Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), no. 4, 427–474 (French, with English summary). MR 660145
Additional Information
- Wlodzimierz Zwonek
- Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland
- Email: zwonek@im.uj.edu.pl
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 199-202
- MSC (1991): Primary 32H15
- DOI: https://doi.org/10.1090/S0002-9939-97-03647-2
- MathSciNet review: 1353411