Tensors | Differential geometry | Tensors in general relativity

Tensor density

In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing from one coordinate system to another (see tensor field), except that it is additionally multiplied or weighted by a power W of the Jacobian determinant of the coordinate transition function or its absolute value. A tensor density with a single index is called a vector density. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. Sometimes tensor densities with a negative weight W are called tensor capacity. A tensor density can also be regarded as a section of the tensor product of a tensor bundle with a density bundle. (Wikipedia).

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Related pages

Covariant derivative | Differential form | Tensor bundle | Tensor product | Pseudotensor | Determinant | Levi-Civita connection | Linear map | Sign function | Change of basis | Section (fiber bundle) | Euclidean space | Tensor | Linear combination | Levi-Civita symbol | Basis (linear algebra) | Metric tensor | Differential geometry | Covariance and contravariance of vectors | Tensor field | Lorentz force