On Bismut flat manifolds

• DOI: 10.1090/tran/8083
• Publication Date: 2020-01-29T09:52:15Z
• Authors: Qingsong Wang; Bo Yang; Fangyang Zheng
• Keywords: Manifold (fluid mechanics)

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