Hermitian connection

Hermitian connection

In mathematics, the Hermitian connection abla, also called the Chern connection, is the unique connection on a Hermitian manifold that satisfies the following conditions,
# It preserves the metric g, i.e., abla g=0.
# It preserves the complex structure J, i.e., abla J=0.
# The torsion is pure in its indices.If the Hermitian manifold admits a symplectic structure, i.e., if it is a Kähler manifold, then the Hermitian connection and the Levi-Civita connection coincide.

References

* Nakahara, Geometry, Topology, and Physics, Taylor & Francis.


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