Estimates of the Kobayashi-Royden metric in almost complex manifolds

Gaussier, Hervé; Sukhov, Alexandre

doi:10.24033/bsmf.2486

Estimates of the Kobayashi-Royden metric in almost complex manifolds
[Estimées de la métrique de Kobayashi-Royden dans les variétés presque complexes]

Gaussier, Hervé ; Sukhov, Alexandre

Bulletin de la Société Mathématique de France, Tome 133 (2005) no. 2, pp. 259-273.

Résumé
Abstract

Nous établissons une estimée inférieure pour la métrique de Kobayashi-Royden sur une variété presque complexe $(M, J)$ admettant une fonction bornée strictement pluri-sous-harmonique. Nous appliquons ce résultat à l’étude du comportement de la métrique au bord d’un domaine strictement pseudoconvexe dans $M$ et donnons une condition suffisante d’hyperbolicité complète d’un domaine dans $(M, J)$ .

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 $(M, J)$ .

MR Zbl | 2 citations dans Numdam

DOI : 10.24033/bsmf.2486

Classification : 32V40, 32V15, 32H40, 32T15, 53C15
Keywords: almost complex manifolds, Kobayashi-Royden metric,

J

-holomorphic discs
Mot clés : variétés presque complexes, métrique de Kobayashi-Royden, disques

J

-holomorphes

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Gaussier, Hervé; Sukhov, Alexandre. Estimates of the Kobayashi-Royden metric in almost complex manifolds. Bulletin de la Société Mathématique de France, Tome 133 (2005) no. 2, pp. 259-273. doi : 10.24033/bsmf.2486. https://www.numdam.org/articles/10.24033/bsmf.2486/

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