In Stephani's "Relativity", section 33.3, equation (33.9), he has the Killing equations for cartesian coordinates as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\xi_{a,b}+\xi_{b,a}=0[/tex]

From there he says upon differentiation, you can get the following three equations

[tex]\xi_{a,bc}+\xi_{b,ac}=0[/tex]

[tex]\xi_{b,ca}+\xi_{c,ba}=0[/tex]

[tex]\xi_{c,ab}+\xi_{a,cb}=0[/tex]

Now, I'm not use to the ,; notation, but doesn't the first equation mean

[tex]\partial_b \xi_a + \partial_a \xi_b=0[/tex]?

If so, I don't understand the other 3 equations then. If for example, the first one is suppose to be subsequent differentiation by [tex]\partial_c[/tex], then wouldn't it be[tex]\xi_{a,b,c}+\xi_{b,a,c}=0[/tex]?

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# Killing vector in Stephani

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