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Ganchev, G. and Ivanov, S. (2001) Harmonic and Holomorphic 1-Forms on Compact Balanced Hermitian Manifolds. Differential Geometry and its Applications, 14, 79-93.
https://doi.org/10.1016/s0926-2245(00)00039-5

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.