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Article

Slovák, Jan
Remark on bilinear operations on tensor fields. (English). Archivum Mathematicum, vol. 56 (2020), issue 5, pp. 301-305
MSC: 53A32, 53A55, 58A20 | MR 4188744 | Zbl 07285967 | DOI: 10.5817/AM2020-5-301
Keywords:
natural operator; tensor field; natural functional; Lie derivative
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.
References:
[1] Čap, Andreas, Slovák, Jan: Infinitesimally natural operators are natural. Differential Geom. Appl. 2 (1) (1992), 45–55. DOI 10.1016/0926-2245(92)90008-B | MR 1244455
[2] Čap, Andreas, Slovák, Jan: On multilinear operators commuting with Lie derivatives. Ann. Global Anal. Geom. 13 (3) (1995), 251–279. DOI 10.1007/BF00773659 | MR 1344482
[3] Janyška, Josef: Remarks on natural differential operators with tensor fields. Arch. Math. (Brno) 55 (2019), 289–308. DOI 10.5817/AM2019-5-289 | MR 4057926
[4] Kolář, Ivan, Michor, Peter W., Slovák, Jan: Natural operations in Differential Geometry. Springer, 1993, vi+434 pp. MR 1202431
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