Question

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

score 53 · Answer 1 · 2026-03-23 15:04:23

53

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 23 Mar 2026 - 15:04

score 179 · Answer 2 · 2026-03-20 14:51:14

179

Views

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

Published on 20 Mar 2026 - 14:51

score 97 · Answer 3 · 2026-03-22 23:45:23

97

Views

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

Published on 22 Mar 2026 - 23:45

score 221 · Answer 4 · 2026-03-22 02:04:51

221

Views

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

Published on 22 Mar 2026 - 2:04

score 103 · Answer 5 · 2026-03-22 17:35:37

103

Views

Averaging of a differential form.

Published on 22 Mar 2026 - 17:35

score 246 · Answer 6 · 2026-03-24 20:32:14

246

Views

Interchanging Duals and Metrics for Riemann Curvature Definition

Published on 24 Mar 2026 - 20:32

score 215 · Answer 7 · 2026-03-21 21:10:07

215

Views

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

Published on 21 Mar 2026 - 21:10

score 383 · Answer 8 · 2026-03-25 03:24:12

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

score 293 · Answer 9 · 2026-03-22 17:59:02

293

Views

Differentiating under the integral sign on a manifold

Published on 22 Mar 2026 - 17:59

score 2.1k · Answer 10 · 2026-03-23 07:49:53

2.1k

Views

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

Published on 23 Mar 2026 - 7:49

score 43 · Answer 11 · 2018-02-15 15:55:08

43

Views

Show equivalence of dot product and differential form surface integrals

Published on 15 Feb 2018 - 15:55

score 278 · Answer 12 · 2026-03-22 12:39:07

278

Views

Complexified cotangent bundle

Published on 22 Mar 2026 - 12:39

score 236 · Answer 13 · 2026-03-24 16:11:19

236

Views

Cartan's vielbein

Published on 24 Mar 2026 - 16:11

score 244 · Answer 14 · 2026-03-20 14:05:43

244

Views

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

Published on 20 Mar 2026 - 14:05

score 98 · Answer 15 · 2018-02-17 21:37:11

98

Views

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

Published on 17 Feb 2018 - 21:37

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?

Trending Questions

Popular # Hahtags

Popular Questions