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Tensor bundle

In mathematics, the tensor bundle of a manifold is the direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold. To do calculus on the tensor bundle a connection is needed, except for the special case of the exterior derivative of antisymmetric tensors.

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Tensor bundle

Nodes16
Edges15
Triples5
Avg. degree1.88
Density0.125
Components1

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Tensor bundle

Top relations

is a · 3
Tensor bundle → fiber bundle V, fiber bundle where the fiber is a tensor product of any number of copies of the tangent space and/or cotangent space of the base space, special kind of vector bundle
related to Definition · 2
Tensor bundle → As, Explicitly

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Important terminology

tensor bundle fiber space displaystyle tangent cotangent isbn oclc mathematics manifold bundles mathematical vol direct sum special tensors calculus connection

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tensor bundleis afiber bundle where the fiber is a tensor product of any number of copies of the tangent space and/or cotangent space of the base space0.90text
Tensor bundleis aspecial kind of vector bundle0.90text
Tensor bundleis afiber bundle V0.90text
Tensor bundlerelated to DefinitionAs0.60section
Tensor bundlerelated to DefinitionExplicitly0.60section

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    Min side: 3
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