Geodesic
Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections
Archivum mathematicum, Tome 34 (1998) no. 2, pp. 229-237 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann $\varepsilon $-connection.
We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann $\varepsilon $-connection.
Classification : 53A55, 53C05
Keywords: covariant differentiation; Christoffel symbols 
@article{ARM_1998_34_2_a1,
     author = {Orta\c{c}gil, Erc\"ument},
     title = {Classical differential geometry with {Christoffel} symbols of {Ehresmann} $\varepsilon $-connections},
     journal = {Archivum mathematicum},
     pages = {229--237},
     year = {1998},
     volume = {34},
     number = {2},
     mrnumber = {1645308},
     zbl = {0910.53006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998_34_2_a1/}
}
TY  - JOUR
AU  - Ortaçgil, Ercüment
TI  - Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections
JO  - Archivum mathematicum
PY  - 1998
SP  - 229
EP  - 237
VL  - 34
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ARM_1998_34_2_a1/
LA  - en
ID  - ARM_1998_34_2_a1
ER  - 
%0 Journal Article
%A Ortaçgil, Ercüment
%T Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections
%J Archivum mathematicum
%D 1998
%P 229-237
%V 34
%N 2
%U http://geodesic.mathdoc.fr/item/ARM_1998_34_2_a1/
%G en
%F ARM_1998_34_2_a1
Ortaçgil, Ercüment. Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections. Archivum mathematicum, Tome 34 (1998) no. 2, pp. 229-237. http://geodesic.mathdoc.fr/item/ARM_1998_34_2_a1/

[1] Birkhof, G. D.: Relativity and Modern Physics. Harvard Press, 1923.

[2] Cartan, E.: Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion. C.R. Acad. Sci. Paris 174, 1922, p. 522.

[3] Crittenden, R.: Covariant differentiation. Quart. J. Math. Oxford Ser. 13, 1962, 285-298. | MR | Zbl

[4] Ehresmann, C.: Sur les connexions d’ordre superieur. Atti del V$^\circ $ Congresso del Unione Mat. Ital., 1955, 344-346.

[5] Eisenhart, L. P.: Riemannian Geometry. Princeton Univ. Press, 1926. | MR | Zbl

[6] Guillemin, V.: The integrability problem for G-structures. Trans. A.M.S., 116, 1965, 544-560. | MR | Zbl

[7] Kolář, I.: On the absolute differentiation of geometric object fields. Annales Polonici Mathematici, 1973, 293-304. | MR

[8] Kolář, I., Michor, P., Slovák, J.: Natural Operations in Differential Geometry. Springer-Verlag, Berlin, Heidelberg, 1993. | MR

[9] Libermann, P.: Connexions d’ordre superieur et tenseurs de structure. Atti del Convegno Internazionale di Geometria Differenziale, Bologna, 1967.

[10] Ortaçgil, E.: Some remarks on the Christoffel symbols of Ehresmann $\varepsilon $-connections. 3$^{rd}$ Meeting on Current Ideas in Mechanics and Related Fields, Segovia (Spain), June 19-23, 1995, Extracta Mathematicae Vol. II, Num. 1, 172–180 (1996). | MR

[11] Ortaçgil, E.: On a differential sequence in geometry. Turkish Journal of Mathematics, 20 (1996), 473–479. | MR

[12] Pommaret, J. F.: Lie Pseudogroups and Mechanics. Gordon and Breach, London, New York, 1988. | MR | Zbl

[13] Pommaret, J. F.: Partial Differential Equations and Group Theory. Kluwer Academic Publishers, Dordrecht, Boston, London, 1994. | MR | Zbl

[14] Szybiak, A.: Covariant differentiation of geometric objects. Rozprawy Mat. 56, Warszawa, 1967. | MR | Zbl

[15] Terng, L.: Natural vector bundles and natural differential operators. American Journal of Math., 100, 1978, 775-828. | MR | Zbl

[16] Veblen, O.: Normal coordinates for the geometry of paths. Proc. N.A.S., Vol. 8, 1922, p. 192.

[17] Veblen, O., Thomas, T. Y.: The geometry of paths. Transaction of A.M.S., Vol. 25, 1923, 551-608. | MR

[18] Veblen, O.: Invariants of Quadratic Differential Forms. Cambridge Tract 24, University Press, Cambridge, 1927.

[19] Yuen, P. C.: Higher order frames and linear connections. Cahiers de Topologie et Geometrie Diff. 13 (3), 1971, 333-370. | MR | Zbl