Timeline for Two ways to differentiate a section of vector bundle
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2014 at 8:39 | comment | added | Ben McKay | Sorry, I should have indicated more clearly: if $\sigma(p)=0$ we can define $d\sigma(p) \in T^*_p M \otimes E_p$, rather than in $T^*_p M \otimes T_{\sigma(p)} E$. | |
| Feb 3, 2014 at 7:43 | comment | added | user45859 | When $\sigma\in\Gamma(E)$ and $\sigma(p)\neq 0$, why can't we define $d\sigma_p$? Since $\sigma$ is a smooth map from $M$ to $E$, $d\sigma_p$ should be a linear map from $T_pM$ to $T_{\sigma(p)}E$. | |
| Feb 3, 2014 at 7:42 | comment | added | abx | I don't understand the last comment: the differential of $\sigma:M\rightarrow E$ is well-defined as $d\sigma (p): T_p(M)\rightarrow T_{\sigma (p)}(E)$. | |
| Feb 3, 2014 at 7:32 | history | answered | Ben McKay | CC BY-SA 3.0 |