Tensor bundle
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Short description: Concept in mathematics
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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.
Definition
A tensor bundle is a 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, which is a manifold. As such, the fiber is a vector space and the tensor bundle is a special kind of vector bundle.
References
- Template:Lee Introduction to Smooth Manifolds
- Template:Saunders The Geometry of Jet Bundles
- Template:Steenrod The Topology of Fibre Bundles 1999
See also
- Spinor bundle – Geometric structure
- Tensor field – Assignment of a tensor continuously varying across a region of space
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