Question

Is the shear of a vector field related to the exterior differential?

score 537 · Answer 1 · 2026-02-23 02:40:28

537

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Is the shear of a vector field related to the exterior differential?

Published on 23 Feb 2026 - 2:40

score 368 · Answer 2 · 2019-03-02 22:35:02

368

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Calculating Pull-Back of a $1$-form.

Published on 02 Mar 2019 - 22:35

score 121 · Answer 3 · 2019-03-03 20:38:49

121

Views

Standard Coordinates and Covectors for Differential Forms

Published on 03 Mar 2019 - 20:38

score 38 · Answer 4 · 2019-03-04 00:34:38

38

Views

Calculus with Differential Forms.

Published on 04 Mar 2019 - 0:34

score 129 · Answer 5 · 2019-03-04 05:16:05

129

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Why is $e^{it}$ a submersion, and what is the relationship between the derivative $\dot h(t)$ and the differential $h_{*,t}$?

Published on 04 Mar 2019 - 5:16

score 767 · Answer 6 · 2019-03-04 06:08:30

767

Views

Does injectivity of dual imply injectivity of pullback by a surjective submersion?

Published on 04 Mar 2019 - 6:08

score 16 · Answer 7 · 2026-03-11 04:47:15

16

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Vector field, difference of partials equals 1

Published on 11 Mar 2026 - 4:47

score 54 · Answer 8 · 2019-03-04 16:32:21

If $f: U \subset \mathbb{R}^{m} \to \mathbb{R}^{n}$ is a differentiable map and $k > m$, $f^{*}\omega = 0$ for each $k$-form $\omega$.

score 41 · Answer 9 · 2019-03-04 23:14:35

$f^{*}\omega = \det(df)dx_{1}\wedge \cdots \wedge dx_{n}$ for $f(x_{1},...,x_{n}) = (y_{1},...,y_{n})$ and $\omega = dy_{1}\wedge \cdots dy_{n}$

score 235 · Answer 10 · 2026-03-25 17:35:28

235

Views

Pulling back $\mathfrak g $-valued 1-forms

Published on 25 Mar 2026 - 17:35

score 62 · Answer 11 · 2026-02-23 01:20:04

62

Views

When solving differential equations using substitution, does it really matter which substitution you choose?

Published on 23 Feb 2026 - 1:20

score 734 · Answer 12 · 2026-03-25 15:57:10

734

Views

Section and pull-back bundle

Published on 25 Mar 2026 - 15:57

score 37 · Answer 13 · 2019-03-07 21:20:49

37

Views

Calculate a Line Integral of differentiable form of degree $1$.

Published on 07 Mar 2019 - 21:20

score 742 · Answer 14 · 2019-03-12 04:50:11

742

Views

Show a particular differential 1-form on $S^1$ is closed but not exact

Published on 12 Mar 2019 - 4:50

score 186 · Answer 15 · 2019-03-12 16:23:26

186

Views

Exterior derivative of a two-form as a divergence times the volume form

Published on 12 Mar 2019 - 16:23

List Question

Is the shear of a vector field related to the exterior differential?

Calculating Pull-Back of a $1$-form.

Standard Coordinates and Covectors for Differential Forms

Calculus with Differential Forms.

Why is $e^{it}$ a submersion, and what is the relationship between the derivative $\dot h(t)$ and the differential $h_{*,t}$?

Does injectivity of dual imply injectivity of pullback by a surjective submersion?

Vector field, difference of partials equals 1

If $f: U \subset \mathbb{R}^{m} \to \mathbb{R}^{n}$ is a differentiable map and $k > m$, $f^{*}\omega = 0$ for each $k$-form $\omega$.

$f^{*}\omega = \det(df)dx_{1}\wedge \cdots \wedge dx_{n}$ for $f(x_{1},...,x_{n}) = (y_{1},...,y_{n})$ and $\omega = dy_{1}\wedge \cdots dy_{n}$

Pulling back $\mathfrak g $-valued 1-forms

When solving differential equations using substitution, does it really matter which substitution you choose?

Section and pull-back bundle

Calculate a Line Integral of differentiable form of degree $1$.

Show a particular differential 1-form on $S^1$ is closed but not exact

Exterior derivative of a two-form as a divergence times the volume form

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