Kobayashi-Royden vs. Hahn pseudometric in ℂ²
نویسندگان
چکیده
منابع مشابه
Kobayashi–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.
متن کاملKobayashi pseudometric on hyperkähler manifolds
The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincaré disk to M is distance-decreasing. Kobayashi has conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove this result for any hyperkähler manifold if it admits a deformation with a Lagrangian fibration, and its...
متن کاملOn 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...
متن کاملEstimates of the Kobayashi-royden Metric in Almost Complex Manifolds
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2000
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-75-3-289-294