Archivio Istituzionale della RicercaIn the present article, we study compact complex manifolds admitting a Hermitian metric which is strong Kähler with torsion (SKT) and Calabi–Yau with torsion (CYT) and whose Bismut torsion is parallel. We first obtain a characterization of the universal cover of such manifolds as a product of a Kähler Ricci-flat manifold with a Bismut flat one. Then, using a mapping torus construction, we provide non-Bismut flat examples. The existence of generalized Kähler structures is also investigated
CYT and SKT manifolds with parallel Bismut torsion / Brienza, Beatrice; Fino, Anna; Grantcharov, Gueo. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - (2024), pp. 1-26. [10.1017/prm.2024.115]
CYT and SKT manifolds with parallel Bismut torsion
Brienza, Beatrice;Fino, Anna;
2024
Abstract
In the present article, we study compact complex manifolds admitting a Hermitian metric which is strong Kähler with torsion (SKT) and Calabi–Yau with torsion (CYT) and whose Bismut torsion is parallel. We first obtain a characterization of the universal cover of such manifolds as a product of a Kähler Ricci-flat manifold with a Bismut flat one. Then, using a mapping torus construction, we provide non-Bismut flat examples. The existence of generalized Kähler structures is also investigated
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https://hdl.handle.net/11583/2994572