Displaying similar documents to “Geometric prequantization of a generalized mechanical system.”

Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.

Jan Kurek, Wlodzimierz M. Mikulski (2006)

Extracta Mathematicae

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We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TM = J (;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σ αω for all real numbers α with α ≠ 0, where ω is the (k)-lift (in the sense of A. Morimoto) of ω to TM.

On implicit Lagrangian differential systems

S. Janeczko (2000)

Annales Polonici Mathematici

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Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).

Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

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Differential forms on the Fréchet manifold ℱ ( S , M ) of smooth functions on a compact k -dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the transgression map Ω p ( M ) → Ω p - k ( ℱ ( S , M ) ) (hat pairing with a constant function) and the bar map Ω p ( M ) → Ω p ( ℱ ( S , M ) ) (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].