한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
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크리스토펠, 리치, 레비-치비타에 의한 19세기 중반부터 20세기 초반까지 미분기하학의 발전

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

  • 투고 : 2015.03.27
  • 심사 : 2015.04.21
  • 발행 : 2015.04.30
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초록

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.

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참고문헌

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