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- Density_on_a_manifold abstract "In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold which can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain trivial line bundle, called the density bundle. An element of the density bundle at x is a function that assigns a volume for the parallelotope spanned by the n given tangent vectors at x.From the operational point of view, a density is a collection of functions on coordinate charts which become multiplied by the absolute value of the Jacobian determinant in the change of coordinates. Densities can be generalized into s-densities, whose coordinate representations become multiplied by the s-th power of the absolute value of the jacobian determinant. On an oriented manifold 1-densities can be canonically identified with the n-forms on M. On non-orientable manifolds this identification cannot be made, since the density bundle is the tensor product of the orientation bundle of M and the n-th exterior product bundle of T*M (see pseudotensor.)".
- Density_on_a_manifold wikiPageID "3428935".
- Density_on_a_manifold wikiPageLength "9047".
- Density_on_a_manifold wikiPageOutDegree "40".
- Density_on_a_manifold wikiPageRevisionID "615730062".
- Density_on_a_manifold wikiPageWikiLink Associated_bundle.
- Density_on_a_manifold wikiPageWikiLink Atlas_(topology).
- Density_on_a_manifold wikiPageWikiLink Category:Manifolds.
- Density_on_a_manifold wikiPageWikiLink Cocycle_(algebraic_topology).
- Density_on_a_manifold wikiPageWikiLink Compact_support.
- Density_on_a_manifold wikiPageWikiLink Conformal_geometry.
- Density_on_a_manifold wikiPageWikiLink Coordinate_chart.
- Density_on_a_manifold wikiPageWikiLink Differentiable_manifold.
- Density_on_a_manifold wikiPageWikiLink Differential_form.
- Density_on_a_manifold wikiPageWikiLink Differential_geometry.
- Density_on_a_manifold wikiPageWikiLink Distribution_(mathematics).
- Density_on_a_manifold wikiPageWikiLink Dual_bundle.
- Density_on_a_manifold wikiPageWikiLink Dual_vector_bundle.
- Density_on_a_manifold wikiPageWikiLink Fiber_bundle.
- Density_on_a_manifold wikiPageWikiLink Frame_bundle.
- Density_on_a_manifold wikiPageWikiLink General_linear_group.
- Density_on_a_manifold wikiPageWikiLink Group_representation.
- Density_on_a_manifold wikiPageWikiLink Integral.
- Density_on_a_manifold wikiPageWikiLink Integration_by_substitution.
- Density_on_a_manifold wikiPageWikiLink Jacobian_determinant.
- Density_on_a_manifold wikiPageWikiLink Jacobian_matrix_and_determinant.
- Density_on_a_manifold wikiPageWikiLink Lebesgue_measure.
- Density_on_a_manifold wikiPageWikiLink Line_bundle.
- Density_on_a_manifold wikiPageWikiLink Local_trivialization.
- Density_on_a_manifold wikiPageWikiLink Lp_space.
- Density_on_a_manifold wikiPageWikiLink Manifold.
- Density_on_a_manifold wikiPageWikiLink Mathematics.
- Density_on_a_manifold wikiPageWikiLink Orientability.
- Density_on_a_manifold wikiPageWikiLink Oriented_manifold.
- Density_on_a_manifold wikiPageWikiLink Parallelepiped.
- Density_on_a_manifold wikiPageWikiLink Partition_of_unity.
- Density_on_a_manifold wikiPageWikiLink Pseudotensor.
- Density_on_a_manifold wikiPageWikiLink Radon_measure.
- Density_on_a_manifold wikiPageWikiLink Riesz_representation_theorem.
- Density_on_a_manifold wikiPageWikiLink Section_(fiber_bundle).
- Density_on_a_manifold wikiPageWikiLink Springer-Verlag.
- Density_on_a_manifold wikiPageWikiLink Springer_Science+Business_Media.
- Density_on_a_manifold wikiPageWikiLink Support_(mathematics).
- Density_on_a_manifold wikiPageWikiLink Tensor_density.
- Density_on_a_manifold wikiPageWikiLink Tensor_product.
- Density_on_a_manifold wikiPageWikiLink Vector_bundle.
- Density_on_a_manifold wikiPageWikiLinkText "1-density".
- Density_on_a_manifold wikiPageWikiLinkText "Density on a manifold".
- Density_on_a_manifold wikiPageWikiLinkText "conformal densities".
- Density_on_a_manifold wikiPageWikiLinkText "densities".
- Density_on_a_manifold wikiPageWikiLinkText "density on a manifold".
- Density_on_a_manifold wikiPageWikiLinkText "density".
- Density_on_a_manifold hasPhotoCollection Density_on_a_manifold.
- Density_on_a_manifold wikiPageUsesTemplate Template:Abs.
- Density_on_a_manifold wikiPageUsesTemplate Template:Citation.
- Density_on_a_manifold wikiPageUsesTemplate Template:Harv.
- Density_on_a_manifold subject Category:Manifolds.
- Density_on_a_manifold type Space.
- Density_on_a_manifold comment "In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold which can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain trivial line bundle, called the density bundle.".
- Density_on_a_manifold label "Density on a manifold".
- Density_on_a_manifold sameAs Dichtebündel.
- Density_on_a_manifold sameAs 밀도_다발.
- Density_on_a_manifold sameAs m.064r7hf.
- Density_on_a_manifold sameAs Q1209467.
- Density_on_a_manifold sameAs Q1209467.
- Density_on_a_manifold wasDerivedFrom Density_on_a_manifold?oldid=615730062.
- Density_on_a_manifold isPrimaryTopicOf Density_on_a_manifold.