Curvature characterization of Hermitian manifolds with Bismut parallel torsion
Differential Geometry
2026-05-19 v3
Abstract
In this article, we study Hermitian manifolds whose Bismut connection has parallel torsion, which will be called {\em Bismut torsion parallel manifolds,} or {\em BTP} manifolds for brevity. We obtain a necessary and sufficient condition characterizing BTP manifolds in terms of Bismut curvature tensor alone (Theorem 1.1). We also present examples and discuss some general properties for BTP manifolds, as well as give a classification result for non-balanced BTP threefolds (Theorem 1.16).
Cite
@article{arxiv.2407.10497,
title = {Curvature characterization of Hermitian manifolds with Bismut parallel torsion},
author = {Quanting Zhao and Fangyang Zheng},
journal= {arXiv preprint arXiv:2407.10497},
year = {2026}
}
Comments
28 pages. This grows out of the first half of the preprint (arXiv: 2208.03071)