Geodesic
Symplectic structure on a~Grassmannian fibration
Sbornik. Mathematics, Tome 66 (1990) no. 2, pp. 439-446

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The author describes a canonical structure on a Grassmannian fibration whose fiber is a Grassmann manifold of the tangent spaces of a smooth manifold. This structure generalizes the symplectic structure on the cotangent bundle. This symplectic form takes its values in a vector space or even in a vector bundle. This structure is canonical; it is uniquely defined by a smooth manifold. Bibliography: 5 titles. 
@article{SM_1990_66_2_a8,
     author = {G. D. Berishvili},
     title = {Symplectic structure on {a~Grassmannian} fibration},
     journal = {Sbornik. Mathematics},
     pages = {439--446},
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_66_2_a8/}
}
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G. D. Berishvili. Symplectic structure on a~Grassmannian fibration. Sbornik. Mathematics, Tome 66 (1990) no. 2, pp. 439-446. http://geodesic.mathdoc.fr/item/SM_1990_66_2_a8/