Timeline for Definition for the Chern–Weil formula?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 19 at 22:17 | history | edited | LSpice | CC BY-SA 4.0 |
Typo
|
| Jun 19 at 20:34 | comment | added | Quarto Bendir | When you replace $K$ by $\lambda$ you get (up to normalization) the integral of $\omega^m$, which is (up to normalization) the volume. (I think this is sometimes called Wirtinger theorem.) The particular constants $r$ and $(m-1)!$ are just normalizations depending on some conventions of how the various quantities are defined. | |
| Jun 19 at 17:14 | comment | added | Nikolai | Thank you for the answer, but I'm not entirely sure how you go from $K_A = \lambda(E)\text{id}$ to the obtained expression for $\lambda(E)$ by the steps you mentioned? Wedging with $\omega^{m-1}$ gives $$\frac{i}{2\pi} K \wedge \omega^{m-1}$$ and integrating over $X$ gives the expression $$\int_X \frac{i}{2\pi} K \wedge \omega^{m-1}$$. @quarto-bendir | |
| Jun 19 at 15:19 | history | answered | Quarto Bendir | CC BY-SA 4.0 |