Timeline for Isn't the following addition wrong on manifold as done in Frankel book?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16, 2020 at 14:25 | vote | accept | aitfel | ||
| Sep 16, 2020 at 14:25 | comment | added | aitfel | Thanks! the quantifier single resolved all of the issues. | |
| Sep 16, 2020 at 14:24 | comment | added | J. Murray | @aitfel You can make the resulting expression act on a function, but it can't be written as the action of a (single) tangent vector at any point of the manifold. In this sense, the "addition" of two tangent vectors at different points does not yield a tangent vector. However in your expression you are subsequently taking the limit as $\phi_t x$ and $x$ coincide, and the result is the action of a well-defined tangent vector $\mathbf X_x$ acting on the function $\mathbf Y(f)$. | |
| Sep 16, 2020 at 14:17 | comment | added | aitfel | Then my assumption that we can't add vector from two different points (Tangent space) is wrong since we can just make the resulting expression act on a function. Or is it just happen that such manipulation won't result in an identity? | |
| Sep 16, 2020 at 14:03 | history | answered | J. Murray | CC BY-SA 4.0 |