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Keywords:
Dirac structure; almost Dirac structure; tangent functor of higher order; natural transformations
Dirac structure; almost Dirac structure; tangent functor of higher order; natural transformations
Summary:
Let $L$ be an almost Dirac structure on a manifold $M$. In [2] Theodore James Courant defines the tangent lifting of $L$ on $TM$ and proves that:
If $L$ is integrable then the tangent lift is also integrable.
In this paper, we generalize this lifting to tangent bundle of higher order.
References:
[1] Cantrijn, F., Crampin, M., Sarlet, W., Saunders, D.: The canonical isomorphism between $T^{k}T^{\ast }$ and $T^{\ast }T^{k}$. C. R. Acad. Sci., Paris, Sér. II 309 (1989), 1509–1514. MR 1033091
[2] Courant, T.: Tangent Dirac Structures. J. Phys. A: Math. Gen. 23 (22) (1990), 5153–5168. DOI 10.1088/0305-4470/23/22/010 | MR 1085863 | Zbl 0715.58013
[3] Courant, T.: Tangent Lie Algebroids. J. Phys. A: Math. Gen. 27 (13) (1994), 4527–4536. DOI 10.1088/0305-4470/27/13/026 | MR 1294955 | Zbl 0843.58044
[4] Gancarzewicz, J., Mikulski, W., Pogoda, Z.: Lifts of some tensor fields and connections to product preserving functors. Nagoya Math. J. 135 (1994), 1–41. MR 1295815 | Zbl 0813.53010
[5] Grabowski, J., Urbanski, P.: Tangent lifts of Poisson and related structures. J. Phys. A: Math. Gen. 28 (23) (1995), 6743–6777. DOI 10.1088/0305-4470/28/23/024 | MR 1381143 | Zbl 0872.58028
[6] Kolář, I., Michor, P., Slovák, J.: Natural Operations in Differential Geometry. Springer-Verlag, 1993. MR 1202431
[7] Morimoto, A.: Lifting of some type of tensors fields and connections to tangent bundles of $p^{r}$-velocities. Nagoya Math. J. 40 (1970), 13–31. MR 0279720
[8] Ntyam, A., Wouafo Kamga, J.: New versions of curvatures and torsion formulas of complete lifting of a linear connection to Weil bundles. Ann. Pol. Math. 82 (3) (2003), 233–240. DOI 10.4064/ap82-3-4 | MR 2040808
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