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 E₁ and E₂ 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.

References

• Ketsetzis, Georgios; Salamon, Simon (2004), "Complex structures on the Iwasawa manifold", Advances in Geometry 4 (2): 165–179, arXiv:math.DG/0112295, doi:10.1515/advg.2004.012 .
• Griffiths, P.; Harris, J. (1994), Principles of Algebraic Geometry, Wiley Classics Library, Wiley Interscience, p. 444, ISBN 0-471-05059-8