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Flat nearly Kähler manifolds

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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 ≥ 3. Moreover, the geometry of the second factor is encoded in a complex three-form \(\zeta \in \Lambda^3 (\mathbb{C}^m)^*\). The first nontrivial example occurs in dimension 4m = 12.

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Authors and Affiliations

  1. Department Mathematik, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Vicente Cortés & Lars Schäfer

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  1. Vicente Cortés
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  2. Lars Schäfer
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Correspondence to Lars Schäfer.

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Cortés, V., Schäfer, L. Flat nearly Kähler manifolds. Ann Glob Anal Geom 32, 379–389 (2007). https://doi.org/10.1007/s10455-007-9068-6

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  • DOI: https://doi.org/10.1007/s10455-007-9068-6

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