# Tagged Questions

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### What exactly is a 0-form?

From what I understand, a k-form in the real numbers is essentially a mapping $\mathbb{R^k} \rightarrow \mathbb{R}$, but I can't seem to find a corresponding definition for a "0-form". Wikipedia seems ...
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### Bogus proof that the Liouville Form on the cotangent bundle is nondegenerate.

Suppose we have a manifold $M$ of dimension $n$ and its cotangent bundle $T^*M$. The Liouville form $\lambda$ on $T^*M$ is defined as $\lambda_{\omega_p} = \pi^*(\omega_p)$ where $\pi$ is the standard ...
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### differential form vanish somewhere on compact orientable without boundary manifold [duplicate]

(a)Let $M =M^n$ a $n-$dimensional compact, orientable, differential manifold without boundary ( $\partial M = \emptyset$). Define $\omega$ a differential $(n-1)-$ form on $M$. Prove that there ...
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### differential form

one form $\alpha$ over a smooth manifold is non vanishing means for every $p\in M$, $\alpha_p\neq 0$. But $\alpha_p$ is linear map $T_M\to \mathbb R$, hence $\alpha_p(0)=0$. So confusion arises ...
### $4$-form $\omega \wedge \omega$ vanishes on $S^4$
If $\omega$ is a closed $2$-form on $S^4$, how can I show the $4$-form $\omega \wedge \omega$ vanishes somewhere on $S^4$? I am guessing that the fact we're talking about the $2$-form being ...