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 $\nabla_{[X,Y]} Du$?
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 $\nabla_{[X,Y]} Du$?