\begin{definition}[Definition:Laplacian/Riemannian Manifold]
Let $\struct {M, g}$ be a Riemannian manifold.
Let $f \in \map {\CC^\infty} M : M \to \R$ be a smooth mapping on $M$.
Let $\grad$ be the gradient operator.
Let $\operatorname {div}$ be the divergence operator.
The '''Laplacian of $f$''' is defined as:
:$\Delta f := \map {\operatorname {div} } {\grad f}$
\end{definition}