We describe all M fm-natural operators S: Q ↝ Symp P1 transforming classical linear connections ∇ on m-dimensional manifolds M into almost symplectic structures S(∇) on the linear frame bundle P1M over M.
@article{bwmeta1.element.doi-10_2478_v10062-009-0005-y,
author = {Anna Bednarska},
title = {Almost symplectic structures on the linear frame bundle from linear connection},
journal = {Annales UMCS, Mathematica},
volume = {63},
year = {2009},
pages = {49-53},
zbl = {1204.58002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0005-y}
}
Anna Bednarska. Almost symplectic structures on the linear frame bundle from linear connection. Annales UMCS, Mathematica, Tome 63 (2009) pp. 49-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0005-y/
Berndt, R., An Introduction to Symplectic Geometry, Graduate Studies in Mathematics, Vol 26, American Mathematical Society, Providence, Rhode Island, 2001. | Zbl 0986.53028
Kobayashi, S., Nomizu, K., Foundations of Differential Geometry, Vol I, Interscience Publisher, New York-London, 1963. | Zbl 0119.37502
Kolář, I., Michor, P. W. and Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. | Zbl 0782.53013
Kurek, J., Mikulski, W. M., Riemannian structures on higher order frame bundles from classical linear connections, Differential Geometry, Proceedings of the VIII International Colloquium Santiago de Compostela, World Scientific 2009, 296-300. | Zbl 1181.58004
León, M. de, Rodrigues, P. R., Methods of Differential Geometry in Analytical Mechanics, North-Holland Math. Stud. 158, Amsterdam, 1989. | Zbl 0687.53001