LIP manifolds: from metric to Finslerian structure
type: Item
instance of: scholarly article
title: LIP manifolds: from metric to Finslerian structure
zbMATH Open document ID: 0819.53014
DOI: 10.1007/BF02571901
author: Giuseppe De Cecco
author: Giuliana Palmieri
published in: Mathematische Zeitschrift
publication date: 1995-05-02T00:00:00Z
full work available at URL: https://eudml.org/doc/174726
review text: In other papers [Math. Z. 207, No. 2, 223-243 (1991; Zbl 0722.58006); Rend. Accad. Naz. Sci. Detta XL, V. Ser. 17, No. 1, 129-151 (1993)] the authors have studied Lipschitz manifolds with Riemannian or Finslerian structure with only measurable coefficients and the intrinsic distance induced by them. In the present paper the following problem is considered: let \(M\) be a LIP manifold with an intrinsic distance, which is locally equivalent to the Euclidean one; what hypotheses are needed in order to endow \(M\) with a Finsler structure \(F\) in such way that \(F\) induces the original given distance? A necessary and sufficient condition is presented. If one starts from a Finsler structure, then its ``derivative'' forms some other Finsler structure, which is stable under the considered procedure.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 737184
zbMATH Keywords: LIP manifolds
zbMATH Keywords: Finsler manifolds
zbMATH Keywords: Lipschitz manifolds
MaRDI profile type: Publication
cites work: Les formes différentielles harmoniques
cites work: Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)
cites work: Integral distance on a Lipschitz Riemannian manifold
cites work: Q3274652
cites work: The index of signature operators on Lipschitz manifolds
description: scientific article; zbMATH DE number 737184