论文标题
在Hermitian歧管上与Bismut-Strominger平行扭转
On Hermitian manifolds with Bismut-Strominger parallel torsion
论文作者
论文摘要
在本文中，我们研究了Hermitian流形的歧管，其bismut-strominger连接具有平行的扭转张量，将其称为{\ em bismut torsion平行流形，}或{\ em btp}歧管。根据曲率张量，我们获得了表征该类别的必要条件。尤其是，bismut平坦或bismutkähler样歧管是{\ em btp}歧管，我们以前的结果已知。我们还获得了非平衡{\ em btp}歧管的结构结果，并获得了非平衡{\ em BTP}三倍和平衡{\ em btp}三倍的分类定理。
In this article, we study Hermitian manifolds whose Bismut-Strominger connection has parallel torsion tensor, which will be called {\em Bismut torsion parallel manifolds,} or {\em BTP} manifolds for short. We obtain a necessary and sufficient condition characterizing this class in terms of the curvature tensor. In particular, Bismut flat or Bismut Kähler-like manifolds are {\em BTP} manifolds, known by our earlier results. We also obtain structural results for non-balanced {\em BTP} manifolds, and classification theorems for non-balanced {\em BTP} threefolds and balanced {\em BTP} threefolds.
