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Mathematics
Differential Geometry
Differential forms on R^n vs. on manifold
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[QUOTE="jbergman, post: 6482219, member: 145841"] I am not sure what the question is. I would say that the answer is no, they are the same as R^n is a manifold. The only thing that changes are the charts that define our manifold. On R^n there happens to be one global chart that is the identity map so that makes things easier. For a general manifold only patches of it are diffeomorphic to R^n so you have charts for these different patches. When doing computations with forms one often needs to work with local coordinates which involves mapping patches of manifold to R^n and doing the computations in the exact same fashion a in R^n. Different patches have different chart maps so that the form can end up being a different function in different charts. So the main differences are this. On a general manifold, you have to do computations in multiple local charts and the local coordinate form can vary form chart to chart. This isn't an issue in R^n. [/QUOTE]
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Differential Geometry
Differential forms on R^n vs. on manifold
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