Curvature characterization of Hermitian manifolds with Bismut parallel torsion

2024/07/15 by Zhao, Quanting, Zheng, Fangyang · 5 citations
#53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.10497

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).

Cited by

• Constant holomorphic sectional curvature conjecture and Fino-Vezzoni conjecture
• Kählerness of compact Hermitian surfaces under semi-definite Strominger-Bismut-Ricci curvatures
• Almost Calabi-Yau with torsion 6-manifolds and the instanton condition
• On balanced Hermitian threefolds with parallel Bismut torsion
• Balanced Bismut torsion-parallel fourfold with constant holomorphic sectional curvature

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