Geodesic
On groups of diffeomorphisms preserving non-degenerate analytic covector fields
Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 741-751

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We consider analytic covector fields on manifolds of even dimension. A field is called non-degenerate if the exterior differential of the corresponding 1-form is a non-degenerate symplectic structure. It is shown that the groups of diffeomorphisms preserving such fields are finite-dimensional and an estimate of their dimension is given. 
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     author = {M. A. Parinov},
     title = {On groups of diffeomorphisms preserving non-degenerate analytic covector fields},
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M. A. Parinov. On groups of diffeomorphisms preserving non-degenerate analytic covector fields. Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 741-751. http://geodesic.mathdoc.fr/item/SM_1995_186_5_a6/