zbMATH — the first resource for mathematics

Remarks on natural differential operators with tensor fields. (English) Zbl 07144744
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.

58A32 Natural bundles
Full Text: DOI arXiv
[1] Čap, A.; Slovák, J., On multilinear operators commuting with Lie derivatives, Ann. Global Anal. Geom. 13 (1995), 251-279
[2] Frölicher, A.; Nijenhuis, A., Theory of vector-valued differential forms, I, II, Nederl. Akad. Wetensch. Proc. Ser. A 59 (1956), 338-350, 351-359
[3] Kolář, I.; Michor, P. W.; Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, 1993
[4] Krupka, D.; Janyška, J., Lectures on Differential Invariants, Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno, 1990
[5] Salimov, A., On operators associated with tensor fields, J. Geom. 99 (2010), 107-145, DOI: 10.1007/s00022-010-0059-6
[6] Schouten, J. A., On the differential operators of first order in tensor calculus, Rapport ZA 1953-012, Math. Centrum Amsterdam (1953), 6 pp
[7] Schouten, J. A., Ricci-Calculus: An Introduction to Tensor Analysis and Its Geometrical Applications, 2nd ed., Springer-Verlag Berlin, Heidelberg, 1954
[8] Yano, K.; Ako, M., On certain operators associated with tensor fields, Kodai Math. Sem. Rep. 20 (1968), 414-436
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.