A note on the Kobayashi-Royden metric for real ellipsoids
نویسندگان
چکیده
منابع مشابه
On the Kobayashi-Royden metric for ellipsoids
The Kobayashi indicatrix (infinitesimal unit ball) of a domain in IE n is known to be a biholomorphic invariant. In particular, if a domain is biholomorphic to a ball, then the indicatrix is the ball. Until the recent deep results of Lempert [4], it was not known to what extent the indicatrix characterizes the domain. Sibony had shown earlier that the indicatrix of any pseudoconvex circular dom...
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We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M, J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M, J).
متن کاملA Note on the Royden Boundary
Recently Loeb and Walsh [3] established several results concerning the Royden boundary in the axiomatic setting. This in effect generalizes theorems about H D-f unctions, Dirichlet-finite harmonic functions on surfaces to Riemannian manifolds, which are the most general carriers of these functions. Their results are however restricted to bounded H D-f unctions. Whether Nakai's [4] characterizat...
متن کاملKobayashi–royden vs. Hahn Pseudometric in C 2
We give a characterization of all cartesian products D1 × D2 ⊂ C for which the Kobayashi–Royden and Hahn pseudometrics coincide. In particular, we show that there exist domains in C for which Kobayashi–Royden and Hahn pseudometrics are different.
متن کاملOn the Zero Set of the Kobayashi–royden Pseudometric of the Spectral Unit Ball
Given A ∈ Ωn, the n-dimensional spectral unit ball, we show that B is a ”generalized” tangent vector at A to an entire curve in Ωn if and only if B is in the tangent cone CA to the isospectral variety at A. If B 6∈ CA, then the Kobayashi–Royden pseudometric is positive at (A;B). In the case of Ω3, the zero set of this metric is completely described.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03647-2