| Title:
|
Commutators of flows and fields (English) |
| Author:
|
Mauhart, Markus |
| Author:
|
Michor, Peter W. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
229-236 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The well known formula $[X,Y]=\tfrac{1}{2}\tfrac{\partial ^2}{\partial t^2}|_0 (^Y_{-t}ø^X_{-t}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms. (English) |
| Keyword:
|
commutators |
| Keyword:
|
flows |
| Keyword:
|
vector fields |
| MSC:
|
37C10 |
| MSC:
|
58F25 |
| idZBL:
|
Zbl 0784.58051 |
| idMR:
|
MR1222291 |
| . |
| Date available:
|
2008-06-06T21:23:12Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107455 |
| . |
| Reference:
|
[FK] Frölicher, A., Kriegl, A.: Linear spaces and differentiation theory.Pure and Applied Mathematics, J. Wiley, Chichester, 1988. MR 0961256 |
| Reference:
|
[KMS] Kolář, I., Michor, P. W., Slovák, J.: Natural operators in differential geometry.to appear, Springer-Verlag. MR 1202431 |
| Reference:
|
[KMa] Kriegl, A., Michor, P. W.: A convenient setting for real analytic mappings.Acta Mathematica 165 (1990), 105–159. MR 1064579 |
| Reference:
|
[KMb] Kriegl, A., Michor, P. W.: Aspects of the theory of infinite dimensional manifolds.Differential Geometry and Applications 1(1) (1991). MR 1244442 |
| Reference:
|
[KMc] Kriegl, A., Michor, P. W.: Foundations of Global Analysis.A book in the early stages of preparation. |
| Reference:
|
[KN] Kriegl, A., Nel, L. D.: A convenient setting for holomorphy.Cahiers Top. Géo. Diff. 26 (1985), 273–309. MR 0796352 |
| Reference:
|
[M] Mauhart, M.: Iterierte Lie Ableitungen und Integrabilität.Diplomarbeit, Universität Wien, 1990. |
| Reference:
|
[T] Terng, Chu Lian: Natural vector bundles and natural differential operators.American J. of Math. 100 (1978), 775–828. MR 0509074 |
| . |
