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Jan 12, 2023 at 20:26 comment added Igor Khavkine Distinguished volume form. $\uparrow$
Jan 12, 2023 at 20:16 comment added amilton moreira @IgorKhavkine in $D F_{\varphi}[h]=\int_M \nabla F_{\varphi}(x) h(x) d x$ , $D F_{\varphi}[h]$ is a number , $h(x)$ is a section of a vector bundle and $\nabla F_{\varphi}(x)$ is a function . We need that $\nabla F_{\varphi}(x)$ be a section of the dual bundle in order that the expression make sense
Jan 12, 2023 at 19:52 comment added Igor Khavkine I may still be misunderstanding your question, but any inclusion $\mathcal{D}(M) \hookrightarrow \mathcal{E}'(M)$ requires a distinguished volume form. If that's not made clear in the article, they must have left it implicit or forgot about it.
Jan 12, 2023 at 18:58 history edited Daniele Tampieri CC BY-SA 4.0
Minor grammar & formatting
Jan 12, 2023 at 18:49 history edited amilton moreira CC BY-SA 4.0
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Jan 12, 2023 at 18:37 comment added amilton moreira @ Igor Khavkine I edited my question.
Jan 12, 2023 at 18:35 history edited amilton moreira CC BY-SA 4.0
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Jan 12, 2023 at 18:28 comment added Igor Khavkine The erratic punctuation in your last paragraph makes it really difficult to understand what your question is. :(
Jan 12, 2023 at 18:03 history edited amilton moreira CC BY-SA 4.0
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Jan 12, 2023 at 17:46 history asked amilton moreira CC BY-SA 4.0