On Bismut Flat Manifolds

Qingsong Wang; Bo Yang; Fangyang Zheng

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arXiv · 1603.07058

On Bismut Flat Manifolds

Qingsong Wang·Bo Yang·Fangyang Zheng

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Abstract

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-K\"ahler surfaces, while central Calabi-Eckmann threefolds are the only simply-connected compact Bismut flat threefolds.

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Qingsong Wang, Bo Yang, Fangyang Zheng. 2016-03-23. On Bismut Flat Manifolds. https://arxiv.org/abs/1603.07058

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