Question

Show that $(\textbf{S}^*\textbf{B})(u,v)=\textbf{B}(\textbf{S}(u,v))\cdot \textbf{N}(u,v) \ du \wedge dv$

score 182 · Answer 1 · 2026-03-29 17:06:53

182

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Show that $(\textbf{S}^*\textbf{B})(u,v)=\textbf{B}(\textbf{S}(u,v))\cdot \textbf{N}(u,v) \ du \wedge dv$

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score 587 · Answer 2 · 2014-12-28 11:41:54

587

Views

Understanding the definition of a pullback of a differential $k$-form and applying it in $1-d$

Published on 28 Dec 2014 - 11:41

score 95 · Answer 3 · 2014-12-28 19:17:47

95

Views

Proving that $\frac{d}{dt}\int \Phi_t^*\omega=\int_{\Phi_t \circ \partial c} i_{\mathbb{X}}\omega$

Published on 28 Dec 2014 - 19:17

score 123 · Answer 4 · 2014-12-28 21:03:03

123

Views

Show $D^2=0$ iff $D=e^{-f}de^{f}$ for some function $f$ , where $D\omega := d\omega+\alpha \wedge \omega $

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score 597 · Answer 5 · 2014-12-29 04:13:24

597

Views

A non-vanishing one form on a manifold of arbitrary dimension

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score 80 · Answer 6 · 2014-12-29 10:04:33

80

Views

Show that $\int_b d\omega=0$ where $b(s,t)=\Phi_s(c(t)) $

Published on 29 Dec 2014 - 10:04

score 1.1k · Answer 7 · 2014-12-30 02:21:47

1.1k

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135

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score 518 · Answer 9 · 2015-01-01 00:50:39

518

Views

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score 405 · Answer 10 · 2026-03-29 10:15:15

405

Views

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score 1.3k · Answer 11 · 2015-01-01 02:57:19

1.3k

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score 359 · Answer 12 · 2015-01-01 07:43:03

359

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score 1.6k · Answer 13 · 2015-01-01 19:36:26

1.6k

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Published on 01 Jan 2015 - 19:36

score 255 · Answer 14 · 2015-01-01 20:21:43

255

Views

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Published on 01 Jan 2015 - 20:21

score 2.9k · Answer 15 · 2015-01-01 22:52:35

2.9k

Views

Compute the contraction of a 1-form with a vector field

Published on 01 Jan 2015 - 22:52

List Question

Show that $(\textbf{S}^*\textbf{B})(u,v)=\textbf{B}(\textbf{S}(u,v))\cdot \textbf{N}(u,v) \ du \wedge dv$

Understanding the definition of a pullback of a differential $k$-form and applying it in $1-d$

Proving that $\frac{d}{dt}\int \Phi_t^*\omega=\int_{\Phi_t \circ \partial c} i_{\mathbb{X}}\omega$

Show $D^2=0$ iff $D=e^{-f}de^{f}$ for some function $f$ , where $D\omega := d\omega+\alpha \wedge \omega $

A non-vanishing one form on a manifold of arbitrary dimension

Show that $\int_b d\omega=0$ where $b(s,t)=\Phi_s(c(t)) $

Understanding de Rham cohomology: geometrically speaking, when is a smooth function closed

Using Poincaré lemma to find the generator $H^1$ of $\mathbb R^2 -\{(0,0)\}$?

Constructing functions such that integral along any closed curve is non-zero

Generators of $H^1(T)$

Applying the Frobenius theorem to a decomposable 2-form

How to determine whether a differential $1$-form is globally welldefined?

Compute the wedge product

What does $\alpha$ be the $1$-form and $\beta$ the $2$-form on $\mathbb{R}^3$ mean?

Compute the contraction of a 1-form with a vector field

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