Timeline for Is there an explanation of analogies between the cross-ratio and the Riemann curvature tensor?
Current License: CC BY-SA 4.0
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| Oct 13, 2018 at 18:54 | comment | added | Dan Petersen | Well, I don't actually know a direct connection between the two. All I'm saying is that $d \log \chi$ and the curvature tensor have the following in common: they are both vectors in a representation of $\mathbb S_4$, and that representation happens to be the irrep corresponding to the partition $[2,2]$. If you write down the right Young symmetrizer you see that the symmetries and the Bianchi identity are exactly the conditions on a vector to transform according to this representation. I would be happy to see a direct link between the two. | |
| Oct 13, 2018 at 16:31 | comment | added | Ivan Izmestiev | Thank you! I agree that $d \log (\chi)$ is a holomorphic 1-form on $M_{0,4}$, but cannot see how the curvature tensor enters the picture. Could you expand on this, please? | |
| Oct 13, 2018 at 10:03 | history | edited | Dan Petersen | CC BY-SA 4.0 |
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| Oct 13, 2018 at 9:32 | history | answered | Dan Petersen | CC BY-SA 4.0 |