3 ms·
The thing with differential forms is that (to me) they look a bit magical (why those sign changes? why alternate?). Only when thinking of volume forms do you be
by pfortuny 6y ago
The thing with differential forms is that (to me) they look a bit magical (why those sign changes? why alternate?). Only when thinking of volume forms do you begin to understand it (the determinant being the paradigm of volume element, etc.).
I think some grassmannian computations would be good in this context but, on the other hand, they would become very cumbersome very soon.
As someone says below: Spivak's Differential Calculus on Manifolds is exceptionally good.
- JadeNB 6y agoIncidentally, I'd argue that the determinant is a paradigm of a covolume element: you feed it a volume element and get out a number. (More technically, it lives in the top exterior power of the cotangent bundle, not of the tangent bundle.)
- pfortuny 6y agoWell yes: it is a volume form certainly. Totally right.