Timeline for Higher order Leibniz rule for higher order tangent space
Current License: CC BY-SA 4.0
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| Nov 11, 2020 at 21:33 | comment | added | alexpglez98 | Thanks. I was thinking that always appears factors of the form $(f-f(p))(g-g(p))...$. Then if $f(p)=g(p)=0$, $v(f\cdot g)=\delta (v)(f,g)$, with the coproduct $\delta: {T^{\square}_p}^rM \longrightarrow {T^{\square}}^{r-1}M \otimes {T^{\square}}^{r-1}M $. It gives us the set of vectors $\{(u_i,w_i)\}$. I think this result it's not very useful. | |
| Nov 11, 2020 at 17:27 | comment | added | Willie Wong | Based on your definition, your $v$ is an order $r$ partial differential operator. The best you can say is that there exists a finite set of pairs $\{(u_i, w_i)\} \subseteq ( T_p^{\Box^{r-1}})^2$ such that $$ v(fg) - v(f)g - f v(g) = \sum u(f)w(g) + u(g)w(f)$$ | |
| Nov 11, 2020 at 10:55 | history | asked | alexpglez98 | CC BY-SA 4.0 |