Journal of Lie Theory

no. 1
Lie derivatives of sections of natural vector bundles
Michor, Peter W.1
1Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria
Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 133-138

Time derivatives of pullbacks and push forwards along smooth curves of diffeomorphisms of sections of natural vector bundles are computed in terms of Lie derivatives along adapted non-autonomous vector fields by extending a key lemma of Mauhart and Michor [Arch. Math., Brno 28 (1992)]. There is also the analogous result about the first non-vanishing derivative of higher order.

Received:
Accepted:
Published online:
DOI: 10.5802/jolt.1422
Classification: 58A32
Keywords: Lie derivative, diffeotopy, natural bundle

Michor, Peter W.  1

1 Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria 
Michor, Peter W. Lie derivatives of sections of natural vector bundles. Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 133-138. doi: 10.5802/jolt.1422
@article{10_5802_jolt_1422,
     author = {Michor, Peter W.},
     title = {Lie derivatives of sections of natural vector bundles},
     journal = {Journal of Lie Theory},
     pages = {133--138},
     year = {2026},
     publisher = {XXXX},
     volume = {36},
     number = {1},
     doi = {10.5802/jolt.1422},
     language = {en},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1422/}
}
TY  - JOUR
AU  - Michor, Peter W.
TI  - Lie derivatives of sections of natural vector bundles
JO  - Journal of Lie Theory
PY  - 2026
SP  - 133
EP  - 138
VL  - 36
IS  - 1
PB  - XXXX
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1422/
DO  - 10.5802/jolt.1422
LA  - en
ID  - 10_5802_jolt_1422
ER  - 
%0 Journal Article
%A Michor, Peter W.
%T Lie derivatives of sections of natural vector bundles
%J Journal of Lie Theory
%D 2026
%P 133-138
%V 36
%N 1
%I XXXX
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1422/
%R 10.5802/jolt.1422
%G en
%F 10_5802_jolt_1422

[1] Bauer, Martin; Michor, Peter W.; Vialard, François-Xavier Unbalanced metric transport (2024)

[2] Kriegl, Andreas; Michor, Peter W. The convenient setting of global analysis, Mathematical Surveys and Monographs, 53, American Mathematical Society, 1997 | DOI | MR | Zbl

[3] Kolář, Ivan; Michor, Peter W.; Slovák, Jan Natural operations in differential geometry, Springer, 1993 | DOI | MR | Zbl

[4] Michor, Peter W. Topics in differential geometry, Graduate Studies in Mathematics, 93, American Mathematical Society, 2008 | DOI | MR | Zbl

[5] Michor, Peter W. Manifolds of differentiable mappings, Shiva Mathematics Series, 3, Shiva Publishing, 1980 | Zbl | MR

[6] Mauhart, Markus; Michor, Peter W. Commutators of flows and fields, Arch. Math., Brno, Volume 28 (1992) no. 3–4, pp. 229-236 | Zbl | MR

[7] Moser, Jürgen On the volume elements on a manifold, Trans. Am. Math. Soc., Volume 120 (1965), pp. 286-294 | DOI | MR | Zbl

[8] Terng, Chuu Lian Natural vector bundles and natural differential operators, Am. J. Math., Volume 100 (1978) no. 4, pp. 775-828 | Zbl | DOI | MR

[9] Weinstein, Alan Symplectic manifolds and their Lagrangian submanifolds, Adv. Math., Volume 6 (1971), pp. 329-346 | Zbl | DOI | MR

Cited by Sources: