  For $2\leq p<4$, we study the $L^p$ norms of restrictions of eigenfunctions
of the Laplace-Beltrami operator on smooth compact $2$-dimensional Riemannian
manifolds. Burq, G\'erard, and Tzvetkov
\cite{BurqGerardTzvetkov2007restrictions}, and Hu \cite{Hu2009lp} found the
eigenfunction estimates restricted to a curve with nonvanishing geodesic
curvatures. We will explain how the proof of the known estimates helps us to
consider the case where the given smooth compact Riemannian manifold has
nonpositive sectional curvatures. For $p=4$, we will also obtain a logarithmic
analogous estimate, by using arguments in Xi and Zhang
\cite{XiZhang2017improved}, Sogge \cite{Sogge2017ImprovedCritical}, and
Bourgain \cite{Bourgain1991Besicovitch}.
