| Title:
|
Remarks on natural differential operators with tensor fields (English) |
| Author:
|
Janyška, Josef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
5 |
| Year:
|
2019 |
| Pages:
|
289-308 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete situations. (English) |
| Keyword:
|
tensor field |
| Keyword:
|
natural differential operator |
| Keyword:
|
Lie derivative |
| Keyword:
|
Yano-Ako operator |
| MSC:
|
53A32 |
| idZBL:
|
Zbl 07144744 |
| idMR:
|
MR4057926 |
| DOI:
|
10.5817/AM2019-5-289 |
| . |
| Date available:
|
2019-12-09T12:22:04Z |
| Last updated:
|
2020-11-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147942 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer–Verlag, 1993. MR 1202431 |
| Reference:
|
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| Reference:
|
[5] Salimov, A.: On operators associated with tensor fields.J. Geom. 99 (2010), 107–145, DOI: 10.1007/s00022-010-0059-6. MR 2823104, 10.1007/s00022-010-0059-6 |
| Reference:
|
[6] Schouten, J.A.: On the differential operators of first order in tensor calculus.Rapport ZA 1953-012, Math. Centrum Amsterdam (1953), 6 pp. MR 0062508 |
| Reference:
|
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| Reference:
|
[8] Yano, K., Ako, M.: On certain operators associated with tensor fields.Kodai Math. Sem. Rep. 20 (1968), 414–436. MR 0234370, 10.2996/kmj/1138845745 |
| . |
