| Title:
|
Remark on bilinear operations on tensor fields (English) |
| Author:
|
Slovák, Jan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
56 |
| Issue:
|
5 |
| Year:
|
2020 |
| Pages:
|
301-305 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This short note completes the results of [3] by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in [3] can be characterized in a completely algebraic way, even without any continuity assumption on the operations. (English) |
| Keyword:
|
natural operator |
| Keyword:
|
tensor field |
| Keyword:
|
natural functional |
| Keyword:
|
Lie derivative |
| MSC:
|
53A32 |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 07285967 |
| idMR:
|
MR4188744 |
| DOI:
|
10.5817/AM2020-5-301 |
| . |
| Date available:
|
2020-11-20T13:58:23Z |
| Last updated:
|
2021-02-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148440 |
| . |
| Reference:
|
[1] Čap, Andreas, Slovák, Jan: Infinitesimally natural operators are natural.Differential Geom. Appl. 2 (1) (1992), 45–55. MR 1244455, 10.1016/0926-2245(92)90008-B |
| Reference:
|
[2] Čap, Andreas, Slovák, Jan: On multilinear operators commuting with Lie derivatives.Ann. Global Anal. Geom. 13 (3) (1995), 251–279. MR 1344482, 10.1007/BF00773659 |
| Reference:
|
[3] Janyška, Josef: Remarks on natural differential operators with tensor fields.Arch. Math. (Brno) 55 (2019), 289–308. MR 4057926, 10.5817/AM2019-5-289 |
| Reference:
|
[4] Kolář, Ivan, Michor, Peter W., Slovák, Jan: Natural operations in Differential Geometry.Springer, 1993, vi+434 pp. MR 1202431 |
| . |
