LIP manifolds: from metric to Finslerian structure
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.
scientific article; zbMATH DE number 737184