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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.

Attributes	Values
rdf:type	Thing
rdfs:label	Complex vector bundle (en) 복소수 벡터 다발 (ko) 複素ベクトル束 (ja) Komplex vektorknippe (sv)
rdfs:comment	미분기하학에서 복소수 벡터 다발(複素數vector다발, 영어: complex vector bundle)은 올이 복소수 벡터 공간의 구조를 갖추는 매끄러운 벡터 다발이다. (ko) 数学において、複素ベクトル束（ふくそベクトルそく、英: complex vector bundle）は、ファイバーが複素ベクトル空間であるようなベクトル束である。任意の複素ベクトル束はによって実ベクトル束と見ることができる。逆に、任意の実ベクトル束 E はによって複素ベクトル束にすることができる。そのファイバーは Ex ⊗R C である。パラコンパクト空間上の任意の複素ベクトル束にはエルミート計量を入れることができる。複素ベクトル束の基本的な不変量はチャーン類である。 (ja) Inom matematiken är en komplex vektorknippe en vektorknippe vars fibrer är komplexa vektorrum. Varje komplex vektorknippe kan ses som en reell vektorknippe gnom restriktion av skalärer. Omvänt kan ur varje reell vektorknippe E konstrueras en komplex vektorknippe med fibrerna Ex ⊗R C. Till varje komplex vektorknippe över ett kan man associera en . Den grundläggande invarianten av en komplex vektorknippe är Chernklassen. (sv) 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)
rdfs:seeAlso	Complex conjugate vector space Linear complex structure
dcterms:subject	Vector bundles
Wikipage page ID	1538109 (xsd:integer)
Wikipage revision ID	1080334752 (xsd:integer)
Link from a Wikipage to another Wikipage	Holomorphic vector bundle Restriction of scalars Complexification Vector bundles Dual bundle K-theory Paracompact space Chern class Vector bundle Euler class Hermitian metric Oriented vector bundle Almost complex structure Real form Real vector bundle Complex vector space Theorem of Newlander and Nirenberg
sameAs	Complex vector bundle Complex vector bundle Complex vector bundle Complex vector bundle Complex vector bundle Complex vector bundle Complex vector bundle
dbp:wikiPageUsesTemplate	dbt:' dbt:Citation dbt:Overline dbt:See_also dbt:Zwnj
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) 미분기하학에서 복소수 벡터 다발(複素數vector다발, 영어: complex vector bundle)은 올이 복소수 벡터 공간의 구조를 갖추는 매끄러운 벡터 다발이다. (ko) 数学において、複素ベクトル束（ふくそベクトルそく、英: complex vector bundle）は、ファイバーが複素ベクトル空間であるようなベクトル束である。任意の複素ベクトル束はによって実ベクトル束と見ることができる。逆に、任意の実ベクトル束 E はによって複素ベクトル束にすることができる。そのファイバーは Ex ⊗R C である。パラコンパクト空間上の任意の複素ベクトル束にはエルミート計量を入れることができる。複素ベクトル束の基本的な不変量はチャーン類である。 (ja) Inom matematiken är en komplex vektorknippe en vektorknippe vars fibrer är komplexa vektorrum. Varje komplex vektorknippe kan ses som en reell vektorknippe gnom restriktion av skalärer. Omvänt kan ur varje reell vektorknippe E konstrueras en komplex vektorknippe med fibrerna Ex ⊗R C. Till varje komplex vektorknippe över ett kan man associera en . Den grundläggande invarianten av en komplex vektorknippe är Chernklassen. (sv)
prov:wasDerivedFrom	wikipedia-en:Complex_vector_bundle?oldid=1080334752&ns=0
page length (characters) of wiki page	4281 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Complex_vector_bundle
is Link from a Wikipage to another Wikipage of	Holomorphic vector bundle Stiefel–Whitney class Chern–Weil homomorphism Orientation of a vector bundle Dual bundle G-spectrum Ginzburg–Landau theory Chern class Hermitian manifold Holomorphic tangent bundle Serre–Swan theorem Vector bundle Complex structure Spinor bundle Spin structure Conjugate bundle
is Wikipage redirect of	Conjugate bundle
is foaf:primaryTopic of	wikipedia-en:Complex_vector_bundle

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