The classification of compact and simply connected PL 4-manifolds states that the homeomorphism classes coincide with the homotopy classes, and that these are classified by the intersection form. We show here that “most” of these classes with an indefinite intersection form can be represented by a tight polyhedral embedding into some Euclidean space. It remains open which of the PL structures c...

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 ζ ∈ Λ3(Cm)∗. The first nontrivial example occurs in dimens...