Jetmetriken und hyperbolische Geometrie. (On jet metrics and hyperbolic geometry)
type: Item
instance of: scholarly article
title: Jetmetriken und hyperbolische Geometrie. (On jet metrics and hyperbolic geometry)
zbMATH Open document ID: 0664.32020
DOI: 10.1007/BF01230277
author: Hans Grauert
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173998
review text: Let E be a unit complex disk and let Y be a complex manifold. Denote by J(m,Y) the jet-bundle over Y of order m. By definition a jetmetric of order m is a continuous non-negative real function on J(m,Y) such that \(f(ca)=| c| f(a)\) on the fibers of the bundle. Starting from f and some non-constant holomorphic map from E to Y it is possible to define some hermitian metric in E. We say that f is hyperbolic if for any holomorphic map from E to Y the induced metric has only isolated zeros on E and has the Gaussian curvature uniformly bounded by a negative constant. Let now Y be a complement of general union of at least three smooth quadrics in a projective plane. It is proved that Y has a hyperbolic metric of order 4.
Mathematics Subject Classification ID: 32Q45
zbMATH DE Number: 4086047
zbMATH Keywords: hyperbolic space
zbMATH Keywords: jet-bundle
zbMATH Keywords: jetmetric
zbMATH Keywords: hyperbolic metric
reviewed by: A. N. Parshin
MaRDI profile type: Publication
cites work: Q3657016
cites work: Hermitesche Metriken und normale Familien holomorpher Abbildungen
cites work: Hyperbolicity of the complement of plane curves
cites work: Function theory on manifolds which possess a pole
cites work: Intrinsic distances, measures and geometric function theory
cites work: Hyperbolic and Diophantine analysis
OpenAlex ID: W2073387776
Recommended article: Q3779005
Recommended article: Über Ähnlichkeit, Dehnung und Schrumpfung in der hyperbolischen Geometrie
Recommended article: Q3616135
Recommended article: Q5342894
Recommended article: Q3715800
Recommended article: Metrisierungstheorie und Jacobiformen. (Metrization theory and Jacobi forms)
Recommended article: Q3472180
Recommended article: Geometry of spaces with the Jacobi metric
Recommended article: Hyperbolic metric, curvature of geodesics and hyperbolic discs in hyperbolic plane domains
description: scientific article; zbMATH DE number 4086047