Anna Fino, Maurizio Parton, Simon Salamon
Published 2002-09-20Version 1
This paper classifies Hermitian structures on 6-dimensional nilmanifolds M=G/L for which the fundamental 2-form is d d-bar closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group, and explicit solutions are obtained from a limacon-shaped curve in the complex plane. Related theory provides examples of various types of Ricci-flat structures.
Journal: Comment. Math. Helv. 79 (2004) 317-340
Anti-self-dual connections over the $5$D Heisenberg group and the twistor method
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