nLab Chern connection

Idea

(…)

Related concepts

• holomorphic vector bundle

References

Lecture notes:

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

• [e-mail]: 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]

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

• Roberto Téllez Domínguez: Chern correspondence for higher principal bundles, Commun. Math. Phys. 406 (2025) 313 [arXiv:2310.12738, doi:10.1007/s00220-025-05490-4]