Flat nearly Kähler manifolds

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 $\zeta \in {\Lambda }^3({\mathbb{C}}^m{)}^{\ast }$. The first nontrivial example occurs in dimension $4m=12$.

14 pages

Cited by in corpus (1)

• Geometric structures on Lie groups with flat bi-invariant metric