  Let $e_\l(x)$ be an eigenfunction with respect to the Laplace-Beltrami
operator $\Delta_M$ on a compact Riemannian manifold $M$ without boundary:
$\Delta_M e_\l=\l^2 e_\l$. We show the following gradient estimate of $e_\l$:
for every $\l\geq 1$, there holds $\l\|e_\l\|_\infty/C\leq \|\nabla
e_\l\|_\infty\leq C{\l}\|e_\l\|_\infty$, where $C$ is a positive constant
depending only on $M$.
