For sequences of warped product metrics on a 3-torus satisfying the scalar curvature bound Rj ≥ − 1 j , uniform upper volume and diameter bounds, and a uniform lower area bound on the smallest minimal surface, we find a subsequence which converges in both the Gromov-Hausdorff (GH) and the Sormani-Wenger Intrinsic Flat (SWIF) sense to a flat 3-torus.Date: May 25, 2018.

Abstract. We characterize HKT structures in terms of a nondegenrate complex Poisson bivector on a hypercomplex manifold. We extend the characterization to the twistor space. After considering the flat case in detail, we show that the twistor space of a hyperkähler manifold admits a holomorphic Poisson structure. We briefly mention the relation to quaternionic and hypercomlex deformations on tori and K3 surfaces.