List questions from differential-forms

59

Views

Find a regular, non-constant, closed curve $\gamma:[0,1] \rightarrow \Bbb R^2$ such that $\int_\gamma x^3dy-y^3dx=0$.

Published on 07 May 2026 - 12:16

192

Views

What does it mean, intuitively, to have a differential form on a Manifold (example inside)

Published on 07 May 2026 - 11:30

104

Views

Finite dimensionality of the "deRham cohomology" defined using $C^{k,\alpha}$ forms instead of smooth forms.

Published on 07 May 2026 - 7:38

235

Views

$\int\limits_C e^{x^2-y^2}(\cos(2xy)dx+\sin(2xy)dy)$ over unit circle

Published on 07 May 2026 - 6:56

112

Views

Averaging of a differential form.

Published on 29 Apr 2026 - 12:47

250

Views

Interchanging Duals and Metrics for Riemann Curvature Definition

Published on 05 May 2026 - 7:14

216

Views

$H^2(\mathbb R^3 \setminus \{0\})$ does not vanish

Published on 25 Mar 2026 - 6:24

383

Views

If integrals of pullbacks of a form only depend on the boundary values, is it exact?

Published on 25 Mar 2026 - 3:24

296

Views

Differentiating under the integral sign on a manifold

Published on 12 Apr 2026 - 23:04

2.1k

Views

Differential forms: $dx \wedge dy$ vs $dx dy$

Published on 25 Mar 2026 - 6:24

46

Views

Show equivalence of dot product and differential form surface integrals

Published on 14 Apr 2026 - 8:24

287

Views

Complexified cotangent bundle

Published on 10 May 2026 - 8:25

238

Views

Cartan's vielbein

Published on 05 Apr 2026 - 11:05

250

Views

Laplace-Beltrami operator in $\mathbb{R}^m$

Published on 29 Apr 2026 - 12:24

101

Views

Why is $\alpha = x^2dx^1 - x^1dx^2$ not a differential of a function?

Published on 16 Apr 2026 - 4:01

List Question

Find a regular, non-constant, closed curve $\gamma:[0,1] \rightarrow \Bbb R^2$ such that $\int_\gamma x^3dy-y^3dx=0$.

What does it mean, intuitively, to have a differential form on a Manifold (example inside)

Finite dimensionality of the "deRham cohomology" defined using $C^{k,\alpha}$ forms instead of smooth forms.

$\int\limits_C e^{x^2-y^2}(\cos(2xy)dx+\sin(2xy)dy)$ over unit circle

Averaging of a differential form.

Interchanging Duals and Metrics for Riemann Curvature Definition

$H^2(\mathbb R^3 \setminus \{0\})$ does not vanish

If integrals of pullbacks of a form only depend on the boundary values, is it exact?

Differentiating under the integral sign on a manifold

Differential forms: $dx \wedge dy$ vs $dx dy$

Show equivalence of dot product and differential form surface integrals

Complexified cotangent bundle

Cartan's vielbein

Laplace-Beltrami operator in $\mathbb{R}^m$

Why is $\alpha = x^2dx^1 - x^1dx^2$ not a differential of a function?

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