Chern connection (changes) in nLab

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Contents

Idea

(…)

• holomorphic vector bundle

References

Lecture notes:

• Andrei Moroianu, Thm. 4.3 in: Lectures on Kähler Geometry, Cambridge University Press 2007 [[arXiv:math/0402223](https://arxiv.org/abs/math/0402223) doi:10.1017/CBO9780511618666, pdf]

• geal2004@cms.zju.edu.cn: Chern connections and Chern curvatures (2008) [pdf]

See also:

• Wikipedia, Hermitian metrics on a holomorphic vector bundle

• Nefton Pali, Chern connections and Chern curvature of the tangent bundle of almost complex manifolds [[arXiv:math/0402028](https://arxiv.org/abs/math/0402028)]

Discussion for holomorphic bundle gerbes with an eye twoards string 2-connections:

• Roberto Tellez-Dominguez, Chern correspondence for higher principal bundles [[arXiv:2310.12738](https://arxiv.org/abs/2310.12738)]