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Families of strong KT structures in six dimensions

Anna Fino·Maurizio Parton·Simon Salamon
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Abstract

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.

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Anna Fino, Maurizio Parton, Simon Salamon. 2002-09-20. Families of strong KT structures in six dimensions. https://arxiv.org/abs/math/0209259

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