Homogeneous k-Symplectic G-Spaces

Azzouz Awane and Michel Goze
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Azzouz Awane: Université Hassan II, Faculté des Sciences
Michel Goze: Université de Haute Alsace, Faculté des Sciences et Techniques

Chapter Chapter 8 in Pfaffian Systems, k-Symplectic Systems, 2000, pp 191-215 from Springer

Abstract: 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 $${L_X}\theta = i(X)d\theta + di(X)\theta $$ 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 $$ i\left( X \right){\theta ^1}, \ldots ,i\left( X \right){\theta ^k} $$ > are closed Pfaffian forms.

Keywords: Hamiltonian System; Heisenberg Group; Smooth Manifold; Hamiltonian Mapping; Momentum Mapping (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-94-015-9526-1_8

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