About: Polyvector field

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A Polyvector field within Mathematics topology is concerned with the properties of a geometric object. A multivector field, polyvector field of degree k , or k-vector field, on a manifold , is a generalization of the notion of a vector field on a manifold.

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rdfs:label	Polyvector field (en)
rdfs:comment	A Polyvector field within Mathematics topology is concerned with the properties of a geometric object. A multivector field, polyvector field of degree k , or k-vector field, on a manifold , is a generalization of the notion of a vector field on a manifold. (en)
dcterms:subject	Differential topology
Wikipage page ID	30067072 (xsd:integer)
Wikipage revision ID	1063555595 (xsd:integer)
Link from a Wikipage to another Wikipage	Vector field Mathematics Mathematical object Tangent bundle Clifford algebra Geometric algebra Topology Differential topology Exterior power Differential topology Tensor field Cotangent bundle Blade (geometry) Differential geometry Manifold Differential forms Multivector Tangent vector Global section
sameAs	Polyvector field Polyvector field
dbp:wikiPageUsesTemplate	dbt:Confusing dbt:Multiple_issues dbt:Reflist dbt:Jargon dbt:Differential-geometry-stub
has abstract	A Polyvector field within Mathematics topology is concerned with the properties of a geometric object. A multivector field, polyvector field of degree k , or k-vector field, on a manifold , is a generalization of the notion of a vector field on a manifold. Whereas a vector field is a global section of tangent bundle, which assigns to each point on the manifold a tangent vector , a multivector field is a section of the kth exterior power of the tangent bundle, , and to each point it assigns a k-vector in . Just as the smooth sections of the tangent bundle (vector fields) make up a vector space, the space of smooth k-vector fields over M make up a vector space . Furthermore, since the tangent bundle is dual to the cotangent bundle, multivector fields of degree k are dual to k-forms, and both are subsumed in the general concept of a tensor field, which is a section of some tensor bundle, often consisting of exterior powers of the tangent and cotangent bundles. A (k,0)-tensor field is a differential k-form, a (0,1)-tensor field is a vector field, and a (0,k)-tensor field is k-vector field. While differential forms are widely studied as such in differential geometry and differential topology, multivector fields are often encountered as tensor fields of type (0,k), except in the context of the geometric algebra (see also Clifford algebra). (en)
prov:wasDerivedFrom	wikipedia-en:Polyvector_field?oldid=1063555595&ns=0
page length (characters) of wiki page	2670 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Polyvector_field
is Link from a Wikipage to another Wikipage of	Lie bialgebroid
is foaf:primaryTopic of	wikipedia-en:Polyvector_field

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