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Volume form

In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold M {\displaystyle M} of dimension n {\displaystyle n} , a volume form is an n {\displaystyle n} -form. It is an element of the space of sections of the line bundle ⋀ n ( T ∗ M ) {\displaystyle \textstyle…

Special cases, Orientation & Divergence

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Overview

Orientation

Relation to measures

Divergence

Special cases

Invariants of a volume form

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Map overview Semantic statistics

Volume form

Nodes76
Edges75
Triples53
Avg. degree1.97
Density0.026316
Components1

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Volume form

Top relations

related to Invariants of a volume form · 9
Volume form → Conversely, Given, In, Intrinsically, Lebesgue, Nikodym, On, Radon, Volume
related to Divergence · 8
Volume form → Given, If, It, Lie, Stokes, The, This, Thus
related to Lie groups · 6
Volume form → As, For, Haar, Lie, That, This
related to Riemannian volume form · 5
Volume form → Any, Here, In, Riemannian, The
related to Symplectic manifolds · 5
Volume form → Any, As, If, Kähler, Riemannian
related to No local structure · 4
Volume form → As, Euclidean, Kobayashi, That
related to Relation to measures · 4
Volume form → Any, Borel, Densities, Given
see also · 4
Volume form → Cylindrical, Generalization, Integration, Line
related to Global structure: volume · 3
Volume form → In, Lebesgue, On
related to Orientation · 3
Volume form → Euclidean, Jacobian, The

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Important terminology

volume form displaystyle manifold omega manifolds measure oriented orientable forms also given symplectic function mathrm thus orientation dx define differentiable

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Volume formis avolume element0.90text
Volume formis aHodge dual of the constant map on the manifold0.90text
Volume formrelated to DivergenceGiven0.60section
Volume formrelated to DivergenceLie0.60section
Volume formrelated to DivergenceIf0.60section
Volume formrelated to DivergenceStokes0.60section
Volume formrelated to DivergenceThe0.60section
Volume formrelated to DivergenceIt0.60section
Volume formrelated to DivergenceThus0.60section
Volume formrelated to DivergenceThis0.60section
Volume formrelated to Global structure: volumeLebesgue0.60section
Volume formrelated to Global structure: volumeOn0.60section

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    Min side: 3
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