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...

Dispersionless bands -- flatbands have been actively studied thanks to their interesting properties and sensitivity perturbations, which makes them natural candidates for exotic states. In parallel non-Hermitian systems attracted much attention in the recent years as a simplified description of open system with gain or loss motivated by potential applications. particular, dispersionless energy ...

Let R be a right GF -closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorenstein ring R, the G...

We present new non-Ricci-flat Kähler metrics with U(N) and O(N) isometries as target manifolds of conformally invariant sigma models with an anomalous dimension. They are so-called Ricci solitons, special solutions to a Ricci-flow equation. These metrics explicitly contain the anomalous dimension and reduce to Ricci-flat Kähler metrics on the canonical line bundles over certain coset spaces in ...

The purpose of this paper is consider some results concerning the special class of the flat manifolds (closed, Riemannian with zero sectional curvature) of dimension n with holonomy groups (Z 2) . In dimension two it is the Klein bottle and in dimension three it is a flat manifold first consider by Hantzsche and Wendt in [4]. Hence we shall call this class of the HantzscheWendt flat manifolds (...

In this article, we thoroughly investigate the stability inequality for Ricci-flat cones. Perhaps most importantly, we prove that the Ricci-flat cone over CP 2 is stable, showing that the first stable non-flat Ricci-flat cone occurs in the smallest possible dimension. On the other hand, we prove that many other examples of Ricci-flat cones over 4-manifolds are unstable, and that Ricci-flat cone...