"If $\omega$ is a 1-form on $\mathbb R^2-0$ such that $d\omega=0$, prove that:$$\omega=\lambda\,d\theta+dg$$for some $\lambda\in\mathbb R$ and $g:\mathbb R^2-0\to\mathbb R$."

Dear oh dear, my math review is getting harder.

Question

"If $\omega$ is a 1-form on $\mathbb R^2-0$ such that $d\omega=0$, prove that:$$\omega=\lambda\,d\theta+dg$$for some $\lambda\in\mathbb R$ and $g:\mathbb R^2-0\to\mathbb R$."

Dear oh dear, my math review is getting harder.

anonymous · Answer

this is blasphemy

agent47 · Answer

this is madness

anonymous · Answer

Don't you dare finish the quote.

anonymous · Answer

THIS IS SPARTAAA

agent47 · Answer

THIS IS SPARTAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!!!!!!!!!!!!!!!!!!!!!!!!!!!

anonymous · Answer

:< Now why would you just go and do that?

anonymous · Answer

While we're at it, can you prove for me that if A is a noetherian ring, and f in A is an element which is neither a zero divisor nor a unit, then every minimal prime ideal containing f has height 1?

Just kidding. That's my sarcastic way of saying "I have no idea wtf this question is about."

anonymous · Answer

Man you and I have gone in two very separate branches of math. I guess you went the path of abstract algebra, topology, Fourier's, etc.? I went analysis, stochastics, statistics, and physics.

anonymous · Answer

Haha nah, I just pulled a random theorem out of chapter one of Hartshorne. Do not ask me why I own a copy of Hartshorne. There is no good reason.

anonymous · Answer

Just typing down random thoughts.

A previous problem motivates the definition:$$c^{*}_{R,1}\omega=\lambda_R(c^{*}_{R,1}\,d\theta)+dg_R$$And then we'll have to define something for positive $R_1,R_2$, so that we can apply Stoke's theorem.

anonymous · Answer

In other words, I have no idea what's going on. I hope this won't be on the GRE.

anonymous · Answer

Man, the notes I took are so weird, I can't understand myself.