Let $(M,g)$ and $(N,h)$ be smooth Riemannian manifolds, with $\dim M=m$, and let
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\begin{align*}
u : M \to N
\end{align*}
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be a smooth harmonic map. Let $\nabla^M$ and $\nabla^N$ denote the Levi-Civita connections of $g$ and $h$, and let $\nabla$ denote the induced connection on the pullback bundle $u^*TN$ and on tensor products involving $T^*M$ and $u^*TN$. Define the energy density