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Results tagged with differential-forms
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user 12482
A differential form $ \omega$ is a section of the exterior algebra $\Lambda^* T^* X$ of a cotangent bundle,
16
votes
Accepted
Hodge decomposition of smooth n-forms: is it an isomorphism of topological vector spaces?
Maybe an even more elementary argument than the one of Tobias:
The continuity of all involved operators is easy: simply all differential operators with smooth coefficients between sections of vector b …
- 8,098
14
votes
Accepted
What do the differential k-forms on a product manifold look like?
Denote by $p_M: M \times N \longrightarrow M$ and $p_N: M \times N \longrightarrow N$ the canonical projections. Then you get an induced bilinear map from $\Omega^i(M) \times \Omega^j(N) \longrightarr …
- 8,098
5
votes
k-form: sum of wedge products of 1-forms?
Johannes' answer can be upgraded to the following statement:
Let $M$ be a second countable and Hausdorff manifold (who cares about others?) and $\pi_i\colon E_i \longrightarrow M$ vector bundles for …
- 8,098