De Cecco, Giuseppe; Palmieri, Giuliana Intrinsic distance on a LIP Finslerian manifold. (Italian. English summary) Zbl 0852.53050 Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat. 17, No. 1, 129-151 (1993). The notion of LIP Finslerian manifold generalizes both the classical Finslerian manifold and the LIP Riemannian manifold. The reason to study LIP Finslerian manifolds is that the distance induced on a LIP Riemannian manifold \((M,g)\) by \(g\), cannot restore \(g\) by differentiation. The example showing the above assertion shows also that a LIP Riemannian metric on the plane cannot be isometrically embedded into any finite-dimensional Euclidean space. Reviewer: C.-L.Bejan (Iaşi) Cited in 6 Documents MSC: 53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) Keywords:intrinsic distance; isometric embedding into Euclidean space; LIP Finslerian manifold; LIP Riemannian manifold PDFBibTeX XMLCite \textit{G. De Cecco} and \textit{G. Palmieri}, Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat. 17, No. 1, 129--151 (1993; Zbl 0852.53050)