Timeline for Etymology “Kulkarni–Nomizu product”
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2023 at 13:23 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https
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| Dec 31, 2022 at 1:22 | comment | added | G. Blaickner | Indeed, that was also what I was wondering. It seems to me that this product in this context has to be known for a much longer time. For example, Kühnel mentions in his book on differential geometry that the Kulkarni-Nomizu product was known as "double transvection" in Ricci calculus. So, this is how I got curious in how this product came to the name "Kulkarni-Nomizu" in the first place. The name seems to be already in use for quite some time. For example, Besse already used it in his book on Einstein manifolds from the 80s. | |
| Dec 30, 2022 at 23:01 | comment | added | Deane Yang | I confess to being a little puzzled why this product wasn't already well known before all this. For one thing, it's the linearization of the Gauss equations $$ R(X,Y,Z,W) = A(X,Z)A(Y,W) - A(X,W)A(Y,Z), $$ where $A$ is the second fundamental form of a hypersurface in Euclidean space. It also appears in formula for the Riemann curvature tensor in terms of the metric. | |
| Dec 30, 2022 at 20:51 | history | edited | LSpice | CC BY-SA 4.0 |
Re-edited in links (see https://mathoverflow.net/questions/437531/etymology-kulkarni-nomizu-product/437537?noredirect=1#comment1127924_437537 and https://mathoverflow.net/questions/437531/etymology-kulkarni-nomizu-product/437537?noredirect=1#comment1127925_437537)
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| Dec 30, 2022 at 20:37 | history | edited | LSpice | CC BY-SA 4.0 |
Oops, missed a typo
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| Dec 30, 2022 at 20:29 | vote | accept | G. Blaickner | ||
| Dec 30, 2022 at 20:23 | history | edited | MyShepherd | CC BY-SA 4.0 |
added 67 characters in body
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| Dec 30, 2022 at 20:22 | history | edited | LSpice | CC BY-SA 4.0 |
Typos; link to Calabi's paper
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| Dec 30, 2022 at 20:18 | history | edited | MyShepherd | CC BY-SA 4.0 |
added 293 characters in body
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| Dec 30, 2022 at 20:12 | history | answered | MyShepherd | CC BY-SA 4.0 |