| Title:
|
Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections (English) |
| Author:
|
Ortaçgil, Ercüment |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
229-237 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
covariant differentiation |
| Keyword:
|
Christoffel symbols |
| MSC:
|
53A55 |
| MSC:
|
53C05 |
| idZBL:
|
Zbl 0910.53006 |
| idMR:
|
MR1645308 |
| . |
| Date available:
|
2009-02-17T10:11:45Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107649 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Crittenden, R.: Covariant differentiation.Quart. J. Math. Oxford Ser. 13, 1962, 285-298. Zbl 0123.15402, MR 0146763 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
[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 1424754 |
| Reference:
|
[11] Ortaçgil, E.: On a differential sequence in geometry.Turkish Journal of Mathematics, 20 (1996), 473–479. MR 1432875 |
| Reference:
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[12] Pommaret, J. F.: Lie Pseudogroups and Mechanics.Gordon and Breach, London, New York, 1988. Zbl 0677.58003, MR 0954613 |
| Reference:
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| Reference:
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[14] Szybiak, A.: Covariant differentiation of geometric objects.Rozprawy Mat. 56, Warszawa, 1967. Zbl 0158.40101, MR 0238208 |
| Reference:
|
[15] Terng, L.: Natural vector bundles and natural differential operators.American Journal of Math., 100, 1978, 775-828. Zbl 0422.58001, MR 0509074 |
| Reference:
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[16] Veblen, O.: Normal coordinates for the geometry of paths.Proc. N.A.S., Vol. 8, 1922, p. 192. |
| Reference:
|
[17] Veblen, O., Thomas, T. Y.: The geometry of paths.Transaction of A.M.S., Vol. 25, 1923, 551-608. MR 1501260 |
| Reference:
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| Reference:
|
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| . |
