About: Tensor product bundle

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In differential geometry, the tensor product of vector bundles E, F (over same space ) is a vector bundle, denoted by E ⊗ F, whose fiber over a point is the tensor product of vector spaces Ex ⊗ Fx. Example: If O is a trivial line bundle, then E ⊗ O = E for any E. Example: E ⊗ E ∗ is canonically isomorphic to the endomorphism bundle End(E), where E ∗ is the dual bundle of E.

Attributes	Values
rdf:type	Thing anatomical structure
rdfs:label	Tensor product bundle (en)
rdfs:comment	In differential geometry, the tensor product of vector bundles E, F (over same space ) is a vector bundle, denoted by E ⊗ F, whose fiber over a point is the tensor product of vector spaces Ex ⊗ Fx. Example: If O is a trivial line bundle, then E ⊗ O = E for any E. Example: E ⊗ E ∗ is canonically isomorphic to the endomorphism bundle End(E), where E ∗ is the dual bundle of E. (en)
dcterms:subject	Differential geometry
Wikipage page ID	46418707 (xsd:integer)
Wikipage revision ID	1020678580 (xsd:integer)
Link from a Wikipage to another Wikipage	Vector-valued differential form Differential geometry Picard group Dual bundle Line bundle Exterior power Tensor field Tensor product of modules Symmetric power Differential form Differential geometry Endomorphism bundle Tensor product of vector spaces Vector bundle
Link from a Wikipage to an external page	http://pi.math.cornell.edu/~hatcher/VBKT/VB.pdf
sameAs	Tensor product bundle Tensor product bundle Tensor product bundle
dbp:wikiPageUsesTemplate	dbt:Distinguish dbt:Reflist dbt:Differential-geometry-stub
has abstract	In differential geometry, the tensor product of vector bundles E, F (over same space ) is a vector bundle, denoted by E ⊗ F, whose fiber over a point is the tensor product of vector spaces Ex ⊗ Fx. Example: If O is a trivial line bundle, then E ⊗ O = E for any E. Example: E ⊗ E ∗ is canonically isomorphic to the endomorphism bundle End(E), where E ∗ is the dual bundle of E. Example: A line bundle L has tensor inverse: in fact, L ⊗ L ∗ is (isomorphic to) a trivial bundle by the previous example, as End(L) is trivial. Thus, the set of the isomorphism classes of all line bundles on some topological space X forms an abelian group called the Picard group of X. (en)
gold:hypernym	Bundle
prov:wasDerivedFrom	wikipedia-en:Tensor_product_bundle?oldid=1020678580&ns=0
page length (characters) of wiki page	2111 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Tensor_product_bundle
is rdfs:seeAlso of	Tensor product Tensor product of modules
is Link from a Wikipage to another Wikipage of	Vector-valued differential form Stable vector bundle Dual bundle Tensor product of line bundles Metric tensor Vector bundle Tensor product of bundles
is Wikipage redirect of	Tensor product of line bundles Tensor product of bundles
is foaf:primaryTopic of	wikipedia-en:Tensor_product_bundle

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