Bochner technique in real Finsler manifolds.
type: Item
instance of: scholarly article
title: Bochner technique in real Finsler manifolds.
zbMATH Open document ID: 1041.53047
DOI: 10.1016/S0252-9602(17)30220-5
author: Tongde Zhong
author: Chunping Zhong
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2003-09-11T00:00:00Z
review text: The non-linear connection associated to Cartan-Finsler connection is used to study the Bochner technique of real Finsler manifolds. Some results about the relations between the vectors and the Ricci curvature of real Finsler manifolds are obtained. De Rham developed a suit of conventional symbols and an efficient method in treating the Laplace operator calculus on manifolds. A sketch of this method for the case of Finsler manifolds and the Weitzenböck formula are given. Using non-linear connections of a Finsler manifold \(M\), the existence of local coordinates, normalized at a point \(x\) is proved, and the Laplace operator \(\Delta \) on 1-forms on \(M\) is defined by nonlinear connection and its curvature tensor. After proving the maximum principle theorem of Hopf-Bochner on \(M\), the Bochner type vanishing theorem of Killing vectors and harmonic 1-form are obtained.
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 58A12
Mathematics Subject Classification ID: 58A14
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 1931034
zbMATH Keywords: Finsler manifold
zbMATH Keywords: Laplace operator
zbMATH Keywords: killing vector field
zbMATH Keywords: harmonic 1-form
zbMATH Keywords: Bochner type vanishing theorem
reviewed by: Irena Comic
MaRDI profile type: Publication
full work available at URL: s0252-9602(17)30220-5
OpenAlex ID: W91362265
description: scientific article; zbMATH DE number 1931034