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http://dx.doi.org/10.14477/jhm.2015.28.2.103

On the Development of Differential Geometry from mid 19C to early 20C by Christoffel, Ricci and Levi-Civita  

Won, Dae Yeon (Dept. of Math., Duksung Women's Univ.)
Publication Information
Journal for History of Mathematics / v.28, no.2, 2015 , pp. 103-115 More about this Journal
Abstract
Contemporary differential geometry owes much to the theory of connections on the bundles over manifolds. In this paper, following the work of Gauss on surfaces in 3 dimensional space and the work of Riemann on the curvature tensors on general n dimensional Riemannian manifolds, we will investigate how differential geometry had been developed from mid 19th century to early 20th century through lives and mathematical works of Christoffel, Ricci-Curbastro and Levi-Civita. Christoffel coined the Christoffel symbol and Ricci used the Christoffel symbol to define the notion of covariant derivative. Levi-Civita completed the theory of absolute differential calculus with Ricci and discovered geometric meaning of covariant derivative as parallel transport.
Keywords
Christoffel symbol; covariant derivative; parallel transport; Christoffel; Ricci-Curbastro; Levi-Civita; Einstein;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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