Classical differential geometry with Christoffel symbols of Ehresmann ε -connections

Ercüment Ortaçgil

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 2, page 229-237
  • ISSN: 0044-8753

Abstract

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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 ε -connection.

How to cite

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Ortaçgil, Ercüment. "Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections." Archivum Mathematicum 034.2 (1998): 229-237. <http://eudml.org/doc/248195>.

@article{Ortaçgil1998,
abstract = {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.},
author = {Ortaçgil, Ercüment},
journal = {Archivum Mathematicum},
keywords = {covariant differentiation; Christoffel symbols; covariant differentiation; Christoffel symbols},
language = {eng},
number = {2},
pages = {229-237},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections},
url = {http://eudml.org/doc/248195},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Ortaçgil, Ercüment
TI - Classical differential geometry with Christoffel symbols of Ehresmann $\varepsilon $-connections
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 2
SP - 229
EP - 237
AB - 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.
LA - eng
KW - covariant differentiation; Christoffel symbols; covariant differentiation; Christoffel symbols
UR - http://eudml.org/doc/248195
ER -

References

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  13. Partial Differential Equations and Group Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1994. Zbl0808.35002MR1308976
  14. Covariant differentiation of geometric objects, Rozprawy Mat. 56, Warszawa, 1967. Zbl0158.40101MR0238208
  15. Natural vector bundles and natural differential operators, American Journal of Math., 100, 1978, 775-828. Zbl0422.58001MR0509074
  16. Normal coordinates for the geometry of paths, Proc. N.A.S., Vol. 8, 1922, p. 192. 
  17. The geometry of paths, Transaction of A.M.S., Vol. 25, 1923, 551-608. MR1501260
  18. Invariants of Quadratic Differential Forms, Cambridge Tract 24, University Press, Cambridge, 1927. 
  19. Higher order frames and linear connections, Cahiers de Topologie et Geometrie Diff. 13 (3), 1971, 333-370. Zbl0222.53033MR0307102

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