All Questions
Tagged with differential-forms dg.differential-geometry
58 questions
5
votes
0
answers
82
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Interpolating from a Hard Lefschetz class to a Kaehler class
Let $X$ be a compact smooth manifold that admits symplectic and Kaehler structures.
There is a paper by Ugarte, Rudyak, Tralle, and Ibanez, showing how the Lefschetz rank can vary along a path of ...
- 191
4
votes
1
answer
455
views
Closed $3$-manifold, $2$-dimensional subbundle of this manifold, is this form exact or not?
Let $M$ be a closed $3$-manifold, and let $\xi$ be a $2$-dimensional subbundle of $TM$. I know the following.
There is a nowhere zero $1$-form $\alpha$ on $M$ with $\alpha(X) = 0$ for any vector ...
- 3,652
14
votes
0
answers
574
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Reference for a proof of the fiberwise Stokes theorem
The fiberwise Stokes theorem says that given a differential form on a smooth fiber bundle whose fibers have boundary,
the difference between the fiberwise integral of the differential and the ...
- 53.3k
6
votes
1
answer
291
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Strange problem about triplets of differential forms
Suppose we have the following map:
$$(\Omega^1(\mathbb{R}^n))^3\longrightarrow(\Omega^2(\mathbb{R}^n))^3$$
$$(\alpha,\beta,\gamma)\longmapsto(\mathrm{d}\alpha+\beta\wedge\gamma,\mathrm{d}\beta+\...
CommunityBot
- 1
3
votes
0
answers
304
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Differential ideals of Pfaffian forms on jet bundles (Integrability)
(I asked this question on math.stackexchange, but got no reaction in several weeks. So, my conclusion is, that it is harder to answer than I thought, and maybe admissible for the attribute 'research ...
- 203
5
votes
3
answers
1k
views
Non-continuous differentiability for differential forms
Generally when working with differential forms, one assumes that they are continuously differentiable, i.e. $C^r$ for some $1\le r \le \infty$. Under this hypothesis, one can define the exterior ...
- 12.1k
2
votes
1
answer
391
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(n-1)-dimensional normal currents and Smirnov's paper
I don't know much about currents, but I saw a paper of Smirnov which seems relevant to a problem I am working on. In the very last paragraph of page 848 of the following paper
http://www.unige.ch/~...
- 21.6k
1
vote
2
answers
675
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$\infty$-forms and $\infty$-plectic geometry
Can you have $\infty$-forms on infinite-dimensional manifolds or elsewhere and what are they used for?
- 6,210