Iwasawa manifold

In mathematics, in the field of differential geometry, an Iwasawa manifold is a compact quotient of a 3-dimensional complex Heisenberg group by a cocompact, discrete subgroup. An 
Iwasawa manifold is a nilmanifold, of real dimension 6.
Iwasawa manifolds give examples where the first two terms "E"1 and "E"2 of the Frölicher spectral sequence are not isomorphic. 
As a complex manifold, such an Iwasawa manifold is an important example of
a compact complex manifold which does not admit any Kähler metric.