  In many problems of PDE involving the Laplace-Beltrami operator on manifolds
with ends, it is often useful to introduce radial or geodesic normal
coordinates near infinity. In this paper, we prove the existence of such
coordinates for a general class of manifolds with ends, which contains
asymptotically conical and hyperbolic manifolds. We study the decay rate to the
metric at infinity associated to radial coordinates and also show that the
latter metric is always conformally equivalent to the metric at infinity
associated to the original coordinate system. We finally give several examples
illustrating the sharpness of our results.
