MTW definition of differential froms made rigorous

[micromass]

Hello guys!

I've been trying to get some intuition for differential forms. I know the formal theory and I know how useful they are. But then I came across the following paper: https://dl.dropboxusercontent.com/u/828035/Mathematics/forms.pdf
It describes an intuition for forms that is very closely related to how forms are described in MTW. It's really nice.

The only problem is that I have no clue how to make this rigorous. So does anybody know some theorems or results that connect the intuitive picture as described in the pdf to the formal theory of forms. In particular, given a $1$-form (or an $n$-form more generally), how does one draw the associated picture in the pdf?

Thanks a lot!

 

[robphy]

I've been working on a way to draw these accurately in 3-D using VRML, Maple, and VPython...
but that's been on the backburner due to different but related projects.

Here is an old conference poster of mine (on an old website of mine [I'm no longer there]).
http://physics.syr.edu/~salgado/papers/VisualTensorCalculus-AAPT-01Sum.pdf .
Have a look at the references listed.

 

[micromass]

Thanks a lot robphy. The references to your conference poster were really helpful. The two books by Burke and Sternberg give really good intuition and explained a lot to me. I think I have finally figured out how to make the pdf in my OP rigorous with the help of your post.