List questions from differential-forms

280

Views

Proof of the fact that one-form $\omega$ satisfies $\int_{S^1} \omega =0$ $\Rightarrow$ $\omega$ is exact.

Published on 15 Apr 2026 - 3:11

51

Views

Energy is a topological invariant

Published on 14 Apr 2026 - 11:47

63

Views

What conditions are necessary for any differential $1$-form to be the differential of a smooth function?

Published on 15 Apr 2026 - 12:52

169

Views

$S^1$-valued function on $T^n$

Published on 15 Apr 2026 - 18:25

97

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If $f(..., v_{i+1}, v_i,...) = −f(..., v_i, v_{i+1},...)$ prove that $f$ is alternating

Published on 16 Apr 2026 - 3:28

55

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$u_j =∑^k_{i=1}a^i_jv_i$ show $f(u_1,...,u_k) = (\text{det} A)f(v_1,..., v_k)$

Published on 16 Apr 2026 - 4:43

269

Views

A k-1 form on a compact, orientable, k dimensional manifold

Published on 14 Apr 2026 - 20:48

241

Views

Norm of Laplacian of a differential form

Published on 17 Apr 2026 - 6:06

86

Views

Understanding a definition of the exterior derivative

Published on 11 Apr 2026 - 13:49

445

Views

Integration of differential form inclusion of $S^2$

Published on 12 Apr 2026 - 16:52

79

Views

Interchange of limits of differential operators on differential forms

Published on 10 Apr 2026 - 1:35

37

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Verification of this integration on forms by two different methods

Published on 08 Apr 2026 - 21:27

211

Views

Existence of $k$-form with nonzero integral

Published on 13 Apr 2026 - 22:13

138

Views

Curl of a Lie bracket of two vector fields

Published on 13 Apr 2026 - 7:38

89

Views

2-Form on $\mathbb{R}^3$ That Restricts to Surface Area 2-Form on Torus?

Published on 15 Apr 2026 - 5:49

List Question

Proof of the fact that one-form $\omega$ satisfies $\int_{S^1} \omega =0$ $\Rightarrow$ $\omega$ is exact.

Energy is a topological invariant

What conditions are necessary for any differential $1$-form to be the differential of a smooth function?

$S^1$-valued function on $T^n$

If $f(..., v_{i+1}, v_i,...) = −f(..., v_i, v_{i+1},...)$ prove that $f$ is alternating

$u_j =∑^k_{i=1}a^i_jv_i$ show $f(u_1,...,u_k) = (\text{det} A)f(v_1,..., v_k)$

A k-1 form on a compact, orientable, k dimensional manifold

Norm of Laplacian of a differential form

Understanding a definition of the exterior derivative

Integration of differential form inclusion of $S^2$

Interchange of limits of differential operators on differential forms

Verification of this integration on forms by two different methods

Existence of $k$-form with nonzero integral

Curl of a Lie bracket of two vector fields

2-Form on $\mathbb{R}^3$ That Restricts to Surface Area 2-Form on Torus?

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