On Bismut flat manifolds

By Qingsong Wang, Bo Yang, Fang Zheng. Transactions of the American Mathematical Society, 2016

65 citations recorded by the source corpus.

In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus the universal cover of such a manifold is a Lie group equipped with a bi-invariant metric and a compatible left invariant complex structure. In particular, isosceles Hopf surfaces are the only Bismut flat compact non-Kähler surfaces, while central Calabi-Eckmann threefolds are the only simply-connected compact Bismut flat threefolds.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8bf8840133539d1152b96ea090d28cb05d87b2de

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In Applied Mathematics

1. Quanting Zhao
2. Fang Zheng

In Geometry and Topology

1. Quanting Zhao
2. Fang Zheng

Citations in the corpus

• Strominger connection and pluriclosed metrics (2019, methodology): “Note that here we adopted the usual notation for curvature tensor, unlike in [43] or [42], where the first two and last two positions were swapped.”