Balanced 6-dim nilmanifolds

What is it about?

The invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the (restricted) holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if J is abelian, then any invariant balanced J-Hermitian structure provides solutions of the Strominger system.

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