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- Hermitian_connection abstract "In mathematics, a Hermitian connection , is a connection on a Hermitian vector bundle over a smooth manifold which is compatible with the Hermitian metric. If the base manifold is a complex manifold, and the Hermitian vector bundle admits a holomorphic structure, then there is a canonical Hermitian connection, which is called the Chern connection which satisfies the following conditions 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".
- Hermitian_connection wikiPageID "19454065".
- Hermitian_connection wikiPageRevisionID "583334539".
- Hermitian_connection hasPhotoCollection Hermitian_connection.
- Hermitian_connection subject Category:Complex_manifolds.
- Hermitian_connection subject Category:Riemannian_geometry.
- Hermitian_connection subject Category:Structures_on_manifolds.
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- Hermitian_connection type ComplexManifolds.
- Hermitian_connection type Conduit103089014.
- Hermitian_connection type Manifold103717750.
- Hermitian_connection type Object100002684.
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- Hermitian_connection type Pipe103944672.
- Hermitian_connection type Structure104341686.
- Hermitian_connection type StructuresOnManifolds.
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- Hermitian_connection comment "In mathematics, a Hermitian connection , is a connection on a Hermitian vector bundle over a smooth manifold which is compatible with the Hermitian metric. If the base manifold is a complex manifold, and the Hermitian vector bundle admits a holomorphic structure, then there is a canonical Hermitian connection, which is called the Chern connection which satisfies the following conditions Its (0, 1)-part coincides with the Cauchy-Riemann operator associated to the holomorphic structure.".
- Hermitian_connection label "Hermitian connection".
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- Hermitian_connection sameAs Q5646449.
- Hermitian_connection sameAs Q5646449.
- Hermitian_connection sameAs Hermitian_connection.
- Hermitian_connection wasDerivedFrom Hermitian_connection?oldid=583334539.
- Hermitian_connection isPrimaryTopicOf Hermitian_connection.