Geodesic
Remark on bilinear operations on tensor fields
Archivum mathematicum, Tome 56 (2020) no. 5, pp. 301-305 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.5817/AM2020-5-301
Classification : 53A32, 53A55, 58A20
Keywords: natural operator; tensor field; natural functional; Lie derivative 
@article{10_5817_AM2020_5_301,
     author = {Slov\'ak, Jan},
     title = {Remark on bilinear operations on tensor fields},
     journal = {Archivum mathematicum},
     pages = {301--305},
     year = {2020},
     volume = {56},
     number = {5},
     doi = {10.5817/AM2020-5-301},
     mrnumber = {4188744},
     zbl = {07285967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2020-5-301/}
}
TY  - JOUR
AU  - Slovák, Jan
TI  - Remark on bilinear operations on tensor fields
JO  - Archivum mathematicum
PY  - 2020
SP  - 301
EP  - 305
VL  - 56
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2020-5-301/
DO  - 10.5817/AM2020-5-301
LA  - en
ID  - 10_5817_AM2020_5_301
ER  - 
%0 Journal Article
%A Slovák, Jan
%T Remark on bilinear operations on tensor fields
%J Archivum mathematicum
%D 2020
%P 301-305
%V 56
%N 5
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2020-5-301/
%R 10.5817/AM2020-5-301
%G en
%F 10_5817_AM2020_5_301
Slovák, Jan. Remark on bilinear operations on tensor fields. Archivum mathematicum, Tome 56 (2020) no. 5, pp. 301-305. doi: 10.5817/AM2020-5-301

[1] Čap, Andreas, Slovák, Jan: Infinitesimally natural operators are natural. Differential Geom. Appl. 2 (1) (1992), 45–55. | DOI | MR

[2] Čap, Andreas, Slovák, Jan: On multilinear operators commuting with Lie derivatives. Ann. Global Anal. Geom. 13 (3) (1995), 251–279. | DOI | MR

[3] Janyška, Josef: Remarks on natural differential operators with tensor fields. Arch. Math. (Brno) 55 (2019), 289–308. | DOI | MR

[4] Kolář, Ivan, Michor, Peter W., Slovák, Jan: Natural operations in Differential Geometry. Springer, 1993, vi+434 pp. | MR

Cité par Sources :