Timeline for Tensor and tensor field differences
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 23, 2021 at 15:57 | comment | added | TimRias | Is multilinear enough here? Doesn't it need to be a morphism of $C^\infty(M)$-modules? | |
| Sep 23, 2021 at 15:48 | history | edited | Shirish | CC BY-SA 4.0 |
added 18 characters in body
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| Sep 23, 2021 at 15:48 | comment | added | Shirish | @mmeent: Thanks for pointing it out! By "kind of map", I'm taking it to mean that I've failed to mention that $T$ is multilinear (maybe you meant something else by that?). As for $\Omega(M)$, I remember first learning it as a "collection of all covector fields on a smooth manifold". If I've missed a subtlety in description, could you let me know and I'll update my answer asap | |
| Sep 23, 2021 at 15:36 | comment | added | TimRias | Your definition of tensor field is missing a specification of what kind of map $T$ is. Your description of $\Omega(M)$ as a set, suggests we are in the category of sets, which clearly is not enough. | |
| Sep 23, 2021 at 11:37 | comment | added | Shirish | @krabbypatty: That's correct. However, personally I wouldn't call it a "physical" description. More of an intuitive mathematical one. | |
| Sep 23, 2021 at 11:31 | comment | added | krabby patty | Ok Thanks. So physically one might say a tensor field at point $x$ is a locally defined tensor, which in your notation is $T_x$ acting on (co-)tangent vector spaces of the point $x$ with respect to the manifold. | |
| Sep 23, 2021 at 11:27 | vote | accept | krabby patty | ||
| Sep 23, 2021 at 11:05 | history | answered | Shirish | CC BY-SA 4.0 |