# Homework Help: Closed form?

1. Jul 19, 2005

### rocket

closed form??

let $$f:u \rightarrow R^n$$ be a differentiable function with a differentiable inverse $$f^{-1}: f(u) \rightarrow R^n$$. if every closed form on u is exact, show that the same is true for f(u).

Hint: if dw=0 and $$f^{\star}w = d\eta,$$ consider $$(f^{-1})^{\star}\eta.$$

i don't know where to start with the problem. what is a closed form? what does it mean that "every closed form on u is exact"?

2. Jul 19, 2005

### HallsofIvy

Well, where did you get the problem? I can't believe that wherever you got the problem (class or text) didn't have a definition of "closed" and "exact" form!

A differential form ω is closed if dω= 0, exact if ω= dφ for some differential form φ. It can be shown that d(dφ)= 0 for any differential form φ so if &omega; is exact then dω= d(d&phi)= 0.

One question you didn't ask: what is $$f^{\star}$$?