This paper classifies Hermitian structures on 6-dimensional nilmanifolds $M = \Gamma\G$ for which the fundamental 2-form is $\partial \overline \partial$-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 is used to provide examples of various types of Ricci-flat structures.

Families of strong KT structures in six dimensions

FINO, Anna Maria;
2004-01-01

Abstract

This paper classifies Hermitian structures on 6-dimensional nilmanifolds $M = \Gamma\G$ for which the fundamental 2-form is $\partial \overline \partial$-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 is used to provide examples of various types of Ricci-flat structures.
2004
79
317
340
Hermitian metric; complex structure; connection; torsion; nilmanifold
A. Fino; M. Parton; S. Salamon
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/5117
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