About: Complex vector bundle

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In mathematics, a complex vector bundle is a vector bundle whose fibers are complex vector spaces. Any complex vector bundle can be viewed as a real vector bundle through the restriction of scalars. Conversely, any real vector bundle E can be promoted to a complex vector bundle, the complexification whose fibers are Ex ⊗R C. Any complex vector bundle over a paracompact space admits a hermitian metric. The basic invariant of a complex vector bundle is a Chern class. A complex vector bundle is canonically oriented; in particular, one can take its Euler class.

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rdfs:label	Complex vector bundle (en)
rdfs:comment	In mathematics, a complex vector bundle is a vector bundle whose fibers are complex vector spaces. Any complex vector bundle can be viewed as a real vector bundle through the restriction of scalars. Conversely, any real vector bundle E can be promoted to a complex vector bundle, the complexification whose fibers are Ex ⊗R C. Any complex vector bundle over a paracompact space admits a hermitian metric. The basic invariant of a complex vector bundle is a Chern class. A complex vector bundle is canonically oriented; in particular, one can take its Euler class. (en)
sameAs	Complex vector bundle Complex vector bundle
dbp:wikiPageUsesTemplate	dbt:' dbt:Citation dbt:Overline dbt:Zwnj
Subject	Vector bundles
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Complex_vector_bundle?oldid=1022403221&ns=0
Wikipage page ID	1538109 (xsd:integer)
page length (characters) of wiki page	4197 (xsd:nonNegativeInteger)
Wikipage revision ID	1022403221 (xsd:integer)
Link from a Wikipage to another Wikipage	Almost complex manifold Vector bundles Dual bundle Change of rings Chern class K-theory Complexification Hermitian manifold Holomorphic vector bundle Orientation of a vector bundle Paracompact space Vector bundle Vector space Euler class Real form (Lie theory)
has abstract	In mathematics, a complex vector bundle is a vector bundle whose fibers are complex vector spaces. Any complex vector bundle can be viewed as a real vector bundle through the restriction of scalars. Conversely, any real vector bundle E can be promoted to a complex vector bundle, the complexification whose fibers are Ex ⊗R C. Any complex vector bundle over a paracompact space admits a hermitian metric. The basic invariant of a complex vector bundle is a Chern class. A complex vector bundle is canonically oriented; in particular, one can take its Euler class. A complex vector bundle is a holomorphic vector bundle if X is a complex manifold and if the local trivializations are biholomorphic. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Complex_vector_bundle
is Wikipage redirect of	Conjugate bundle
is Link from a Wikipage to another Wikipage of	Ginzburg–Landau theory Dual bundle Chern class Chern–Weil homomorphism Complex structure Hermitian manifold Holomorphic tangent bundle Holomorphic vector bundle G-spectrum Conjugate bundle
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Complex_vector_bundle

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