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

Jerzy Kurek, Wlodzimierz M. Mikulski

  • We describe all canonical 2-forms ?(?) on the r-th order tangent bundle TrM = Jr0 (R;M) of a symplectic manifold (M, ?). As a corollary we deduce that all canonical symplectic structures ?(?) on TrM over a symplectic manifold (M, ?) are of the form ?(?) = Srk=0 ak?(k) for all real numbers ak with ar ? 0, where ?(k) is the (k)-lift (in the sense of A. Morimoto) of ? to TrM.

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