# Tagged Questions

For questions about differential forms which commonly arise in differential geometry, and sometimes in multivariable calculus.

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### Example of exact form

Consider the differential 1-form $\omega = ydx+dy$. I need to show that this is not exact, and find an example of a function $G(x,y)$ such that $G\omega=G(x,y)(ydx+dy)$ is an exact form. I have done ...
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### Theorem 10.22 from PMA RUdin

We know that $(dy_I)_T=dt_{i_1}\land \dots \land dt_{i_k}$ and using definition 10.18 we get $$d((dy_{I})_{T})=d1\land dt_{i_1}\land \dots \land dt_{i_k}=0$$ since $dc=0$ for any $c\in \mathbb{R}^1$. ...
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### Confusion about holomorphic differential on elliptic curve

Let $(a:b)\in\mathbb{C}P^1$ and look at the elliptic curve $C$ given by $y^2=x^3+a^4x+b^6$. It is well known that on this elliptic curve we have the holomorphic differential $dx/y$. I have two ...
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### Nowhere $0$ form on the sphere?

Consider the differential form on $\mathbb R^3$ given by $x dy \wedge dz + y dz \wedge dx + z dx \wedge dy$. I converted this to spherical coordinates using a laborious calculation, and when I'm done,...
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### Pullback of a complex $1$-form
Let $p = \operatorname{exp} : \mathbb{C} \to \mathbb{C}^*$ be a covering and $(U,z)$ a chart of $\mathbb{C}^*$ with $z = x + iy$. Let $\omega = dz/z$ be a one-form on $U$. Problem: Find the pullback \$...