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--- lie_derivative [2023/06/19 12:52] – [In terms of a covariant derivative] spencer
+++ lie_derivative [2023/06/19 12:52] (current) – [In terms of a covariant derivative] spencer
@@ Line 43: / Line 43: @@
 $$(\nabla_{e_i} \omega^j)(e_k) = -\omega^j( \gamma^\ell_{ik} e_\ell) = -\gamma^j_{ik}.$$
 Thus
-$$\nabla_{e_i} \omega^j} = -\gamma^j_{ik} \omega^k.$$
+$$\nabla_{e_i} \omega^j = -\gamma^j_{ik} \omega^k.$$
 So
-$$L_{\partial r} (\omega^i) = -\gamma^i_{nk} \omega^k + \lambda^i \omega^i.$$
+$$L_{\partial_r} (\omega^i) = -\gamma^i_{nk} \omega^k + \lambda^i \omega^i.$$