In mathematics, a Hermitian connection
- Its (0, 1)-part coincides with the Cauchy-Riemann operator associated to the holomorphic structure.
- Its curvature form is a (1, 1)-form.
In particular, if the base manifold is Kähler and the vector bundle is its tangent bundle, then the Chern connection coincides with the Levi-Civita connection of the associated Riemannian metric.
References
Hermitian connection Wikipedia(Text) CC BY-SA