Abstract
Let M be an n(k + 1)-dimensional manifold equipped with a k-symplectic structure (θ 1,..., θ k; E). Let F be the foliation defined by the sub-bundle E. By the relationship
for every ω ∈ p(M) we see that the ollowing properties are equivalent:
-
1.
\({L_X}{\theta^1} = ... = {L_X}{\theta^k} = 0\);
-
2.
\( i\left( X \right){\theta ^1}, \ldots ,i\left( X \right){\theta ^k} \) are closed;
where L is the Lie derivative with respect to X. Then a necessary and sufficient condition for an infinitesimal automorphism X of F to be a Hamiltonian system is that
> are closed Pfaffian forms.
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© 2000 Springer Science+Business Media Dordrecht
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Awane, A., Goze, M. (2000). Homogeneous k-Symplectic G-Spaces. In: Pfaffian Systems, k-Symplectic Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9526-1_8
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DOI: https://doi.org/10.1007/978-94-015-9526-1_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5486-9
Online ISBN: 978-94-015-9526-1
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