On Symplectically Harmonic Forms on Six-dimensional Nilmanifolds

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dc.creatorIbáñez, R.
dc.creatorRudyak, Yu.
dc.creatorTralle, A.
dc.creatorUgarte, L.
dc.date2000-02-07
dc.date.accessioned2026-07-07T04:33:38Z
dc.date.available2026-07-07T04:33:38Z
dc.descriptionIn the present paper we study the variation of the dimensions $h_k$ of spaces of symplectically harmonic cohomology classes (in the sense of Brylinski) on closed symplectic manifolds. We give a description of such variation for all 6-dimensional nilmanifolds equipped with symplectic forms. In particular, it turns out that certain 6-dimensional nilmanifolds possess families of homogeneous symplectic forms $ω_t$ for which numbers $h_k(M,ω_t)$ vary with respect to t. This gives an affirmative answer to a question raised by Boris Khesin and Dusa McDuff. Our result is in contrast with the case of 4-dimensional nilmanifolds which do not admit such variations by a remark of Dong Yan.
dc.identifierhttps://arxiv.org/abs/math/0002053
dc.identifierhttp://arxiv.org/abs/math/0002053
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58647
dc.subjectSymplectic Geometry
dc.subject53C15
dc.titleOn Symplectically Harmonic Forms on Six-dimensional Nilmanifolds
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