The Euler-Lagrange Cohomology Groups on Symplectic Manifolds

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dc.creatorGuo, Han-Ying
dc.creatorPan, Jianzhong
dc.creatorWu, Ke
dc.creatorZhou, Bin
dc.date2003-04-20
dc.date.accessioned2026-07-07T05:49:05Z
dc.date.available2026-07-07T05:49:05Z
dc.descriptionThe definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},ω)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the corresponding de Rham cohomology groups $H_{dR}^1({\cal M}^{2n})$ and $H_{dR}^{2n-1}({\cal M}^{2n})$, respectively. The other Euler-Lagrange cohomology groups are different from either the de Rham cohomology groups or the harmonic cohomology groups on $({\cal M}^{2n},ω)$, in general. The general volume-preserving equations on $({\cal M}^{2n},ω)$ are also presented from cohomological point of view. In the special cases, these equations become the ordinary canonical equations in the Hamilton mechanics. Therefore, the Hamilton mechanics has been generalized via the cohomology.
dc.description20 pages, no figures
dc.identifierhttps://arxiv.org/abs/physics/0304074
dc.identifierhttp://arxiv.org/abs/physics/0304074
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/85266
dc.subjectClassical Physics
dc.titleThe Euler-Lagrange Cohomology Groups on Symplectic Manifolds
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