I know that covariant derivative of metric is zero [source, and my lecture notes confirm this]: $$\nabla _{\mu}g_{\alpha \beta} = 0,$$ How can I know if $$\nabla _{\mu}g^{\alpha \beta} = 0?$$
2026-03-25 23:38:13.1774481893
Is the covariant derivative of the inverse metric zero?
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