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

다국어 초록 (Multilingual 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.

참고문헌 (Reference)

1 김영욱, "엘리 카르탕과 20세기 리만기하학" 한국수학사학회 22 (22): 13-26, 2009

2 "수학계보프로젝트"

3 "미국 프린스턴 고등연구소(Institute for Advanced Study) 의 홈페이지의 바일 소개"

4 "맥튜터수학사기록보관소"

5 한길준, "리이만의 생애와 그의 업적에 대한 역사적 소고" 한국수학사학회 24 (24): 61-70, 2011

6 조민식, "리만기하학에서 구면정리의 발전과 역사" 한국수학사학회 24 (24): 23-35, 2011

7 박창균, "로바체프스키의 수학철학과 비유클리드기하" 한국수학사학회 24 (24): 21-31, 2011

8 B. Riemann, "Über die Hypothesen, welche der Geometrie zu Grunde liegen" 13 : 1-15, 1867

9 "Wikipedia"

10 E. Christoffel, "Ueber die Transformation der homogenen Differentialausdrücke zweiten Grades" 70 : 46-70, 1869

11 P. Nastasi, "Toward a scientific and personal biography of Tullio Levi-Civita (1873–1941)" 32 : 203-236, 2005

12 M. Giovanelli, "The forgotten tradition: how the logical empiricists missed the philosophical significance of the work of Riemann, Christoffel and Ricci" 78 : 1219-1257, 2013

13 D. Struik, "The History of Modern Mathematics" Academic Press 99-105, 1989

14 J. Faran, "The Equivalence Problem for Complex Finsler Hamiltonians" 196 : 133-143, 1996

15 T. Levi-Civita, "The Absolute Differential Calculus" Dover 1977

16 T. Levi-Civita, "Sulle trasformazioni delle equazioni Dinamiche" 24 : 255-300, 1896

17 G. Ricci, "Principi di una teoria delle forme differenziali quadratiche" 12 (12): 135-167, 1884

18 S. S. Chern, "On Finsler Geometry" 314 : 757-761, 1992

19 T. Levi-Civita, "Nozione di parallelismo in una varietà qualunque et conseguente specificazione geometrica della curvatura Riemanniana" 42 : 173-205, 1917

20 T. Levi-Civita, "Méthodes de calcul différentiel absolu et leurs applications" 54 : 125-201, 1900

21 S. S. Chern, "Local Equivalence and Euclidean Connections in Finsler Spaces" A5 : 95-121, 1948

22 L. Bianchi, "Lezioni di geometria differenziale" Spoerri 1894

23 G. Ricci, "Le calcul différentiel absolu" 16 : 135-167, 1892

24 A. Guerraggio, "Italian Mathematics between the two World Wars" Birkhäuser 2005

25 C. F. Gauss, "Disquisitiones generales circa superficies curvas" 6 : 99-146, 1827

26 A. Einstein, "Die Grundlage der allgemeinen Relativitätstheorie" 49 : 769-822, 1916

27 G. Ricci, "Di alcune applicazioni del Calcolo differenziale assoluto alla teoria delle forme differenziali quadratiche binarie e dei sistemi a due variabili’, Atti dell’Istituto Veneto discienze" 7 : 167-189, 1893

28 D. Laugwitz, "Bernhard Riemann 1826–1866: turning points in the conception of Mathematics" Birkhäuser 1997

29 P. Butzer, "An outline of the life and work of E. B. Christoffel" 8 : 243-276, 1981

30 D. Bao, "An Introduction to Riemann–Finsler Geometry" Springer-Verlag 2000