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

Eigenfunctions restriction estimates for curves with nonvanishing geodesic curvatures in compact Riemannian surfaces with nonpositive curvature