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I am going through a calculation where we have in hand... $\nabla_Y Du = -QY + \lambda Y,$ where $u$ and $\lambda$ are smooth real valued functions on a manifold $M$ and $Q$ is the Ricci operator. Then what is the value of $\nabla_{[X,Y]} Du$?

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  • $\begingroup$ According to me $\nabla_{[X,Y]}Du=(XY-YX)Du$ $\endgroup$ Commented Jul 10, 2016 at 15:44

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