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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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volume form displaystyle manifold omega manifolds measure oriented orientable forms also given symplectic function mathrm thus orientation dx define differentiable
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Volume form | is a | volume element | 0.90 | text |
| Volume form | is a | Hodge dual of the constant map on the manifold | 0.90 | text |
| Volume form | related to Divergence | Given | 0.60 | section |
| Volume form | related to Divergence | Lie | 0.60 | section |
| Volume form | related to Divergence | If | 0.60 | section |
| Volume form | related to Divergence | Stokes | 0.60 | section |
| Volume form | related to Divergence | The | 0.60 | section |
| Volume form | related to Divergence | It | 0.60 | section |
| Volume form | related to Divergence | Thus | 0.60 | section |
| Volume form | related to Divergence | This | 0.60 | section |
| Volume form | related to Global structure: volume | Lebesgue | 0.60 | section |
| Volume form | related to Global structure: volume | On | 0.60 | section |
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