On the Kobayashi metric for perturbations of the ball
type: Item
instance of: scholarly article
title: On the Kobayashi metric for perturbations of the ball
zbMATH Open document ID: 0789.32014
DOI: 10.1007/BF02571653
author: Leslie Kay
published in: Mathematische Zeitschrift
publication date: 1994-04-12T00:00:00Z
full work available at URL: https://eudml.org/doc/174482
review text: The infinitesimal Kobayashi metric at 0 is studied for smooth \((C^ k,k \geq 6)\) perturbations of the ball in \(\mathbb{C}^ n\); the notion of a first- order hermitian flow is defined. A first-variation formula with an intuitive geometric interpretation is computed for the Kobayashi metric. This is used to derive integro-differential equations whose solutions are the first-order hermitian flows. If a flow is both first-order hermitian and first-order circular, the real normal component of its variation vector field is a linear combination of the real parts of type (1,1) quadratic polynomials.
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 58E11
zbMATH DE Number: 549728
zbMATH Keywords: Kobayashi metric
zbMATH Keywords: hermitian flow
MaRDI profile type: Publication
cites work: On the Kobayashi-Royden metric for ellipsoids
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cites work: Holomorphic retracts and intrinsic metrics in convex domains
cites work: Holomorphic invariants, normal forms, and the moduli space of convex domains
cites work: Q5723628
OpenAlex ID: W2084424467
description: scientific article; zbMATH DE number 549728