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.