- #1
dwellexity
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I need to prove that $$D_\mu D_\nu \xi^\alpha = - R^\alpha_{\mu\nu\beta} \xi^\beta$$ where D is covariant derivative and R is Riemann tensor. ##\xi## is a Killing vector.
I have proved that $$D_\mu D_\nu \xi_\alpha = R_{\alpha\nu\mu\beta} \xi^\beta$$
I can't figure out a way to get the required form from my solution. Please suggest a way to get the required form from my solution.
I have proved that $$D_\mu D_\nu \xi_\alpha = R_{\alpha\nu\mu\beta} \xi^\beta$$
I can't figure out a way to get the required form from my solution. Please suggest a way to get the required form from my solution.