Flat nearly Kähler manifolds
Flat nearly Kähler manifolds
We classify flat strict nearly K\ahler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-K\ahler factor of maximal dimension and a strict flat nearly K\ahler manifold of split signature $(2m,2m)$ with $m\ge 3$. Moreover, the geometry of the second factor is encoded in …