  We give estimates for the $L^p$ norm ($2\leq p \leq +\infty$) of the
restriction to a curve of the eigenfunctions of the Laplace Beltrami operator
on a Riemannian surface. If the curve is a geodesic, we show that on the sphere
these estimates are sharp. If the curve has non vanishing geodesic curvature,
we can improve our results. We also show how our approach apply to higher
dimensional manifolds.
