Symplectically Harmonic Cohomology of Nilmanifolds
نویسنده
چکیده
which is a symplectic analog of the well-known de Rham–Hodge ∗operator on oriented Riemannian manifolds: one should use the symplectic form instead of the Riemannian metric. Going further, one can define operator δ = ± ∗ d∗, δ = 0. The form α is called symplectically harmonic if dα = 0 = δα. However, unlike de Rham–Hodge case, there exist simplectically harmonic forms which are exact. Because of this, Brylinski [2] defined the symplectically harmonic cohomology H hr(−) by setting
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