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arXiv · 2208.03071

On Hermitian manifolds with Bismut-Strominger parallel torsion

Quanting Zhao·Fangyang Zheng
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Abstract

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 K\"ahler-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.

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Quanting Zhao, Fangyang Zheng. 2022-08-05. On Hermitian manifolds with Bismut-Strominger parallel torsion. https://arxiv.org/abs/2208.03071

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