On Symplectically Harmonic Forms on Six-dimensional Nilmanifolds
Symplectic Geometry
2007-05-23 v1
Abstract
In the present paper we study the variation of the dimensions 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 for which numbers 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.
Keywords
Cite
@article{arxiv.math/0002053,
title = {On Symplectically Harmonic Forms on Six-dimensional Nilmanifolds},
author = {R. Ibáñez and Yu. Rudyak and A. Tralle and L. Ugarte},
journal= {arXiv preprint arXiv:math/0002053},
year = {2007}
}