| Title:
|
Natural operators in the view of Cartan geometries (English) |
| Author:
|
Panák, Martin |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
57-75 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove, that $r$-th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order $(1,0)$ (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order $r-1$. On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem is given for the reductive and torsion free geometries. (English) |
| Keyword:
|
Cartan geometry |
| Keyword:
|
gauge natural bundle |
| Keyword:
|
natural operator |
| Keyword:
|
natural sheaf |
| Keyword:
|
reductive Cartan geometry |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1112.58301 |
| idMR:
|
MR1982212 |
| . |
| Date available:
|
2008-06-06T22:41:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107854 |
| . |
| Reference:
|
[CS] Čap, A., Slovák, J.: Infinitesimally natural operators are natural.Differential Geometry and its Applications 2 (1992) 45–55. MR 1244455 |
| Reference:
|
[CSS] Čap, A., Souček, V., Slovák, J.: Almost Hermitian Symmetric Structures I.(1994), ESI preprint. |
| Reference:
|
[Eck] Eck D. J.: Natural sheaves.Illinois J. Math. 31 (1987), 200–207. Zbl 0602.58004, MR 0882109 |
| Reference:
|
[K] Kobayashi, S.: Transformation groups in differential geometry.Springer, 1972. Zbl 0246.53031, MR 0355886 |
| Reference:
|
[KM] Kriegel, A., Michor, P. W.: The convenient setting of global analysis.AMS, SURV 53. 1997. |
| Reference:
|
[KMS] Kolář, I., Michor, P., Slovák, J.: Natural operations in differential geometry.Springer, Berlin New York, 1993. MR 1202431 |
| Reference:
|
[KN] Kobayashi, S., Nomizu, K.: Foundations of differential geometry.Interscience Publishers, New York, London, 1963. MR 0152974 |
| Reference:
|
[P] Panák, M.: Natural operators on the bundle of Cartan connections.Proceedings of the Conference Differential Geometry and Applications, Brno, 1998, 285–292. MR 1708916 |
| Reference:
|
[S] Sharpe, R W.: Differential geometry.Springer, New York-Berlin-Heidelberg, 1997. Zbl 0876.53001, MR 1453120 |
| . |
