Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Volume_form> ?p ?o }
- Volume_form abstract "In mathematics, a volume form on a differentiable manifold is a nowhere-vanishing top-dimensionial form (i.e., a differential form of top degree). Thus on a manifold M of dimension n, a volume form is an n-form, a section of the line bundle Ωn(M) = Λn(T∗M), that is nowhere equal to zero. A manifold has a volume form if and only if it is orientable. An orientable manifold has infinitely many volume forms, since multiplying a volume form by a non-vanishing function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density.A volume form provides a means to define the integral of a function on a differentiable manifold. In other words, a volume form gives rise to a measure with respect to which functions can be integrated by the appropriate Lebesgue integral. The absolute value of a volume form is a volume element, which is also known variously as a twisted volume form or pseudo-volume form. It also defines a measure, but exists on any differentiable manifold, orientable or not.Kähler manifolds, being complex manifolds, are naturally oriented, and so possess a volume form. More generally, the nth exterior power of the symplectic form on a symplectic manifold is a volume form. Many classes of manifolds have canonical volume forms: they have extra structure which allows the choice of a preferred volume form. Oriented Riemannian manifolds and pseudo-Riemannian manifolds have an associated canonical volume form.".
- Volume_form wikiPageID "1855811".
- Volume_form wikiPageLength "13260".
- Volume_form wikiPageOutDegree "81".
- Volume_form wikiPageRevisionID "670588500".
- Volume_form wikiPageWikiLink 1-form.
- Volume_form wikiPageWikiLink Absolute_continuity.
- Volume_form wikiPageWikiLink Absolutely_continuous.
- Volume_form wikiPageWikiLink Almost_symplectic_manifold.
- Volume_form wikiPageWikiLink Atlas_(topology).
- Volume_form wikiPageWikiLink Borel_set.
- Volume_form wikiPageWikiLink Calculus.
- Volume_form wikiPageWikiLink Category:Determinants.
- Volume_form wikiPageWikiLink Category:Differential_forms.
- Volume_form wikiPageWikiLink Category:Integration_on_manifolds.
- Volume_form wikiPageWikiLink Compact_support.
- Volume_form wikiPageWikiLink Complex_manifold.
- Volume_form wikiPageWikiLink Complex_plane.
- Volume_form wikiPageWikiLink Coordinate_atlas.
- Volume_form wikiPageWikiLink Cotangent_bundle.
- Volume_form wikiPageWikiLink Covering_map.
- Volume_form wikiPageWikiLink Covering_space.
- Volume_form wikiPageWikiLink Cylindrical_coordinate_system.
- Volume_form wikiPageWikiLink Deformation_retract.
- Volume_form wikiPageWikiLink Degenerate_bilinear_form.
- Volume_form wikiPageWikiLink Density_on_a_manifold.
- Volume_form wikiPageWikiLink Determinant.
- Volume_form wikiPageWikiLink Diffeomorphism.
- Volume_form wikiPageWikiLink Differentiable_manifold.
- Volume_form wikiPageWikiLink Differential_form.
- Volume_form wikiPageWikiLink Differential_geometry.
- Volume_form wikiPageWikiLink Divergence.
- Volume_form wikiPageWikiLink Divergence_theorem.
- Volume_form wikiPageWikiLink Exterior_algebra.
- Volume_form wikiPageWikiLink Exterior_power.
- Volume_form wikiPageWikiLink Fluid_mechanics.
- Volume_form wikiPageWikiLink Frame_bundle.
- Volume_form wikiPageWikiLink Function_(mathematics).
- Volume_form wikiPageWikiLink G-structure.
- Volume_form wikiPageWikiLink General_linear_group.
- Volume_form wikiPageWikiLink Group_(mathematics).
- Volume_form wikiPageWikiLink Group_action.
- Volume_form wikiPageWikiLink Haar_measure.
- Volume_form wikiPageWikiLink Hodge_dual.
- Volume_form wikiPageWikiLink Integral.
- Volume_form wikiPageWikiLink Jacobian_determinant.
- Volume_form wikiPageWikiLink Jacobian_matrix_and_determinant.
- Volume_form wikiPageWikiLink Kähler_manifold.
- Volume_form wikiPageWikiLink Lebesgue_integral.
- Volume_form wikiPageWikiLink Lebesgue_integration.
- Volume_form wikiPageWikiLink Lebesgue_measure.
- Volume_form wikiPageWikiLink Levi-Civita_symbol.
- Volume_form wikiPageWikiLink Levi-Civita_tensor.
- Volume_form wikiPageWikiLink Lie_derivative.
- Volume_form wikiPageWikiLink Lie_group.
- Volume_form wikiPageWikiLink Line_bundle.
- Volume_form wikiPageWikiLink Linear_frame_bundle.
- Volume_form wikiPageWikiLink Local_coordinates.
- Volume_form wikiPageWikiLink Manifold.
- Volume_form wikiPageWikiLink Manifold_with_boundary.
- Volume_form wikiPageWikiLink Mathematics.
- Volume_form wikiPageWikiLink Measure_(mathematics).
- Volume_form wikiPageWikiLink Metric_tensor.
- Volume_form wikiPageWikiLink Moving_frame.
- Volume_form wikiPageWikiLink Nondegeneracy.
- Volume_form wikiPageWikiLink One-form.
- Volume_form wikiPageWikiLink Orientability.
- Volume_form wikiPageWikiLink Orientable.
- Volume_form wikiPageWikiLink Orientation_(mathematics).
- Volume_form wikiPageWikiLink Orientation_(vector_space).
- Volume_form wikiPageWikiLink Poincaré_metric.
- Volume_form wikiPageWikiLink Positive_real_numbers.
- Volume_form wikiPageWikiLink Positive_reals.
- Volume_form wikiPageWikiLink Principal_bundle.
- Volume_form wikiPageWikiLink Principal_homogeneous_space.
- Volume_form wikiPageWikiLink Pseudo-Riemannian_manifold.
- Volume_form wikiPageWikiLink Pseudotensor.
- Volume_form wikiPageWikiLink Pullback.
- Volume_form wikiPageWikiLink Pullback_(differential_geometry).
- Volume_form wikiPageWikiLink Radon–Nikodym_derivative.
- Volume_form wikiPageWikiLink Radon–Nikodym_theorem.
- Volume_form wikiPageWikiLink Riemannian_manifold.
- Volume_form wikiPageWikiLink Section_(fiber_bundle).
- Volume_form wikiPageWikiLink Solenoidal.
- Volume_form wikiPageWikiLink Solenoidal_vector_field.
- Volume_form wikiPageWikiLink Spherical_coordinate_system.
- Volume_form wikiPageWikiLink Stokes_theorem.
- Volume_form wikiPageWikiLink Support_(mathematics).
- Volume_form wikiPageWikiLink Symplectic_form.
- Volume_form wikiPageWikiLink Symplectic_manifold.
- Volume_form wikiPageWikiLink Symplectic_vector_space.
- Volume_form wikiPageWikiLink Torsor.
- Volume_form wikiPageWikiLink Vector_field.
- Volume_form wikiPageWikiLink Vector_flow.
- Volume_form wikiPageWikiLink Volume_element.
- Volume_form wikiPageWikiLinkText "Volume form".
- Volume_form wikiPageWikiLinkText "Volume form#Riemannian volume form".
- Volume_form wikiPageWikiLinkText "pseudoform".
- Volume_form wikiPageWikiLinkText "surface element".
- Volume_form wikiPageWikiLinkText "volume density".