  We consider the focusing quintic nonlinear Schr\"odinger equation posed on a
rotationally symmetric surface, typically the sphere $S^2$ or the two
dimensional hyperbolic space $H^2$. We prove the existence and the stability of
solutions blowing up on a suitable curve with the log log speed. The Euclidean
case is handled in Rapha\"el (2006) and our result shows that the log log rate
persists in other geometries with the assumption of a radial symmetry of the
manifold.
