Hermitian Finsler metrics and the Kobayashi metric
type: Item
instance of: scholarly article
title: Hermitian Finsler metrics and the Kobayashi metric
zbMATH Open document ID: 0709.53020
published in: Journal of Differential Geometry
publication date: 1990-01-01T00:00:00Z
review text: Given two Hermitian Finsler metrics, the author shows when we can obtain one from the other by a local bihomolomorphic change of coordinates. This problem is solved by using the method of equivalence due to E. Cartan [\textit{R. B. Gardner}, The method of equivalence and its applications, CBMS-NSF Regional Conference Series in Applied Mathematics, 58 (1989; Zbl 0694.53027)]. The second order invariants of smooth Hermitian Finsler metrics are interpreted here. The structure equations of the connection and the Euler-Lagrange equations of the length functional in terms of the connection are also given. The last result contains the converse of \textit{L. Lempert}'s theorem [Bull. Soc. Math. Fr. 109, 427-474 (1981; Zbl 0492.32025)] and it finds some differential conditions which imply that the Finsler metric is the Kobayashi metric of the underlying manifold.
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 32C15
zbMATH DE Number: 4165923
zbMATH Keywords: Hermitian Finsler metrics
zbMATH Keywords: method of equivalence
zbMATH Keywords: connection
zbMATH Keywords: length functional
zbMATH Keywords: Kobayashi metric
Wikidata QID: Q115182224
author: James J. V. Faran
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214444630
OpenAlex ID: W1547433964
DOI: 10.4310/JDG/1214444630
description: scientific article; zbMATH DE number 4165923