All Questions
Tagged with differential-forms dg.differential-geometry
58 questions
3
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answers
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About Frobenius's theorem for differential forms
My question is about a particular case of Frobenius's theorem that states the complete integrability condition for a Pfaff system. Namely,
when dealing with a system reduced to a single 1-form, the ...
- 327
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+\...
- 2,091
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?
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14
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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 ...
- 37.8k
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/~...
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
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 ...
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0
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0
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84
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Application of $k$-forms to differential equations
I was presented with a problem that, in my view, is somewhat difficult, and it relates $k$-forms to systems of differential equations.
Consider the ellipsoid, given by
$$f(u, v)=(a\sin(u) \cos(v), b \...
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