CYT and SKT manifolds with parallel Bismut torsion

Abstract

In the present paper, we study compact complex manifolds admitting a Hermitian metric which is SKT and CYT and whose Bismut torsion is parallel. We first obtain a characterization of the universal cover of such manifolds as a product of a Kaehler Ricci-flat manifold with a Bismut flat one. Then, using a mapping torus construction, we provide non-Bismut flat examples. The existence of generalized Kaehler structures is also investigated.

20 pages. Final version. To appear in Proc. Roy. Soc. Edinburgh Sect.A

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Cited by in corpus (1)

• Some remarks on strong ${\mathrm{G}}_2$-structures with torsion