Displaying similar documents to “On the geometry of the standard k -symplectic and Poisson manifolds.”

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.

Ellipticity of the symplectic twistor complex

Svatopluk Krýsl (2011)

Archivum Mathematicum

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For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the...