| Title:
|
Connections of higher order and product preserving functors (English) |
| Author:
|
Gancarzewicz, Jacek |
| Author:
|
Rahmani, Noureddine |
| Author:
|
Salgado, Modesto |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
889-896 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider a product preserving functor $\mathcal F$ of order $r$ and a connection $\Gamma $ of order $r$ on a manifold $M$. We introduce horizontal lifts of tensor fields and linear connections from $M$ to $\mathcal F(M)$ with respect to $\Gamma $. Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order. (English) |
| Keyword:
|
connections of higher order |
| Keyword:
|
product preserving functors |
| Keyword:
|
lifts of tensors and connections |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1020.53012 |
| idMR:
|
MR1940068 |
| . |
| Date available:
|
2009-09-24T10:58:04Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127773 |
| . |
| Reference:
|
[1] L. Cordero, C. T. J. Dodson and N. de León: Differential Geometry of Frame Bundles.Kluwer Acad. Publ., Dordrecht, 1988. |
| Reference:
|
[2] J. Gancarzewicz: Connections of order $r$.Ann. Polon. Math. 34 (1977), 69–83. Zbl 0347.53008, MR 0440471, 10.4064/ap-34-1-69-83 |
| Reference:
|
[3] J. Gancarzewicz, S. Mahi and N. Rahmani: Horizontal lift of tensor fields of type $(1,1)$ from a manifold to its tangent bundle of higher order.Rend. Circ. Mat. Palermo Suppl. 14 (1987), 43–59. MR 0920845 |
| Reference:
|
[4] J. Gancarzewicz, W. Mikulski and Z. Pogoda: Lifts of tensor fields and linear connections to a product preserving functor.Nagoya Math. J. 135 (1994), 1–41. MR 1295815, 10.1017/S0027763000004931 |
| Reference:
|
[5] J. Gancarzewicz and M. Salgado: Horizontal lifts of tensor fields to the tangent bundle of higher order.Rend. Circ. Mat. Palermo Suppl. 21 (1989), 151–178. MR 1009570 |
| Reference:
|
[6] J. Gancarzewicz and M. Salgado: Connections of higher order and product preserving functors.IMUJ Preprint no 1997/21, e.-publ. http://www/im.uj.edu.pl. |
| Reference:
|
[7] I. Kolář, P. Michor and J. Slovák: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[8] R. Palais and C.-L. Terng: Natural bundles have a finite order.Topology 16 (1977), 271–277. MR 0467787, 10.1016/0040-9383(77)90008-8 |
| Reference:
|
[9] K. Yano and S. Ishihara: Horizontal lifts from manifolds to its tangent bundle.J. Math. Mech. 16 (1967), 1015–1030. MR 0210029 |
| Reference:
|
[10] K. Yano and S. Ishihara: Tangent and Cotangent Bundles: Differential Geometry.Marcel Dekker, New York, 1973. MR 0350650 |
| . |
