Let $M$ be a manifold, $E$ some vector bundle on that manifold and $\nabla$ a covariant derivative on $M \rightarrow E$. Let $N$ be another manifolds and $f \in C^{\infty}(M,N)$.
How can we define $\nabla f$ then?
I know that for some $g \in C^{\infty}(M)$, $\nabla_X g=X(g)$ be what if the function is not $\mathbb{R}$ valued?
I am asking to understand the definition of a wave equation on manifolds as defined here:
