A mapping tori construction of strong HKT and generalized hyperkähler manifolds
Beatrice Brienza, Anna Fino, Gueo Grantcharov
TL;DR
The paper addresses constructing compact manifolds with strong HKT and generalized hyperkähler geometry that are not products of a hyperkähler manifold with a compact Lie group. It develops a mapping torus approach using hyperkähler isometries to lift hyperkähler data to strong HKT on the mapping torus, yielding a parallel torsion form $H$ but nontrivial Bismut curvature. The main results show that $N_ au imes S^3$ carries a strong HKT and a generalized hyperkähler structure, with an explicit Fermat quartic K3 example illustrating a nontrivial compact case; the torsion is parallel yet the construction yields non–Bismut-flat instances. This work broadens the suite of compact strong HKT examples beyond homogeneous spaces, offering a flexible method to generate non-product quaternionic geometries relevant for both mathematics and string-theoretic contexts.
Abstract
In the present paper we provide a construction via mapping tori of (non Bismut flat) strong HKT and generalized hyperkähler structures on compact manifolds. The skew-symmetric torsion is parallel, but the manifolds are not a product of a hyperkähler manifold and a compact Lie group.