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Flat nearly Kähler manifolds

Vicente Cortés·Lars Schäfer
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Abstract

We classify flat strict nearly Kähler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-Kähler factor of maximal dimension and a strict flat nearly Kähler manifold of split signature $(2m,2m)$ with $m\ge 3$. Moreover, the geometry of the second factor is encoded in a complex three-form $ζ\in Λ^3 (\mathbb{C}^m)^*$. The first nontrivial example occurs in dimension $4m=12$.

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Vicente Cortés, Lars Schäfer. 2006-10-05. Flat nearly Kähler manifolds. https://arxiv.org/abs/math/0610176

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