6 papers on mathematics, especially differential geometry

Lipschitz, Rudolf

Publication Date: 1872

About this Item

Lipschitz, Rudolf (1832-1903). Group of 6 papers on mathematics, as listed below. Various sizes. V.p., 1856-72. Disbound or with front wrappers present; see below for detailed condition statements. First Separate Editions. Lipschitz is best known for the "Lipschitz condition" attached to the Cauchy-Lipschitz existence theorem, and for his important series of papers on n-dimensional differential forms, which he began publishing in journals in 1869. "In this area he was one of the direct followers of Riemann, who in his lecture of 1854, before the Gottingen philosophical faculty, had formulated the principal problems of differential geometry in higher-dimension manifolds and had begun the study of the possible metric structure of an n-dimensional manifold. . . . With E. B. Christoffel, [Lipschitz] was one of the first to employ cogredient differentiation; and in the process he created an easily used computational method. He showed that the vanishing of a certain expression is a necessary and sufficient condition for a Riemannian manifold to be Euclidean" (DSB). Lipschitz's extensive investigations of n-dimensional differential forms, and the related areas of the calculus of variations, geometry and mechanics, is one of the foundations of tensor analysis. Lipschitz's work was continued by G. Ricci, whose absolute differential calculus Einstein began using in 1913. DSB. Klein, Mathematical Thought, pp. 718; 899. 1. Untersuchung einer aus vier Elementen gebildeten Reihe. Offprint from J. reine u. angewandte Math. 54 (1856). 16pp. Disbound. Some foxing. 2. Disamina della possibilite d'integrare competamente un dato sistema di equazioni differenziali ordinarie. Offprint from Ann. matematica pura ed applicata, series 2, 2 (1868). 15pp. Original printed front wrapper, back wrapper lacking. 3. Untersuchungen in Betreff der ganzen homogenen Functionen von n Differentialen. Offprint from J. reine u. angewandte Math. 70 (1869). 34pp. Disbound. Some foxing. 4. Entwickelung einiger Eigenschaften der quadratischen Formen von n Differentialen. Erste (zweite) Mittheilung). Offprint from J. reine u. angewandte Math. 71 (1870). 23pp. Disbound. 5. Sopra la teoria della inversione di un sistema di funzioni. Offprint from Ann. matematica pura ed applicata, series 2, 4 (1870). 21pp. Original printed front wrapper; back wrapper lacking. 6. Fortgesetzte Untersuchungen in Betreff der ganzen homogenen Functionen von n Differentialen. Offprint from J. reine u. angewandte Math. 72 (1871). 56pp. Disbound. .

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Bibliographic Details

• Title: 6 papers on mathematics, especially differential geometry
• Publication Date: 1872
• Binding: Soft cover