  We determine accurate asymptotics for the low-lying eigenvalues of the Robin
Laplacian when the Robin parameter goes to $-\infty$. The two first terms in
the expansion have been obtained by K. Pankrashkin in the $2D$-case and by K.
Pankrashkin and N. Popoff in higher dimensions. The asymptotics display the
influence of the scalar curvature and the splitting between every two
consecutive eigenvalues. The analysis is based on the approach developed by
Fournais-Helffer for the semi-classical magnetic Laplacian. We also propose a
WKB construction as a candidate for the ground state energy.
