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Barbaro, G. (2023) On the Curvature of the Bismut Connection: Bismut-Yamabe Problem and Calabi-Yau with Torsion Metrics. The Journal of Geometric Analysis, 33, Article No. 153.
https://doi.org/10.1007/s12220-023-01203-2

has been cited by the following article:

• TITLE: The Connection 1-Form on Hermitian Manifolds

  AUTHORS: Xingliang Liao

  KEYWORDS: Complex Manifolds, Hermitian Structure, Kähler Form, Connection 1-Form

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.2, February 5, 2026

  ABSTRACT: This article studies Hermitian structure on complex manifolds. We introduce the torsion of the Chern connection on Hermitian manifolds and present a global result with the Kähler form related to the torsion coefficients with respect to the connection 1-form. On compact Hermitian manifolds, by introducing a linear operator and, based on it, establishing a duality of differential operators on ( p,q ) -forms, we prove an identity between the Kähler form and the connection 1-forms. Furthermore, we show that the integral of the Kähler form can be explicitly expressed via the connection 1-form and vanishes under the Gauduchon condition.