Timeline for Decomposition of forms on a Spin$(7)$ manifold
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2023 at 12:53 | comment | added | Partha | I see, noted. Thanks! | |
| Aug 11, 2023 at 12:52 | vote | accept | Partha | ||
| Aug 11, 2023 at 12:48 | comment | added | Robert Bryant | @Partha: However, the usual convention (which is mine also) is that the volume form on $\mathbb{R}\times M$ is $\mathrm{d}t\wedge\mathrm{vol}(M)$. If you look at Harvey and Lawson's definition of the $\mathrm{Spin}(7)$ form in terms of the $\mathrm{G}_2$ form, you'll see that their convention agrees with this; their $4$-form is $\mathrm{d}t \wedge\sigma + {\ast}_\sigma\sigma$ where $\sigma$ is the $3$-form on $M$. | |
| Aug 11, 2023 at 12:38 | comment | added | Partha | I see, shouldn't $\gamma$ be $+*\beta$, for $\alpha_7$ to be self dual? My volume form on $M\times\mathbb{R}$ is vol$(M)\wedge dt$. | |
| Aug 11, 2023 at 1:55 | history | answered | Robert Bryant | CC BY-SA 4.0 |