  In this paper we extend the previous convergence results on the generalized
alternating projection method, from subspaces [arXiv:1703.10547], to include
smooth manifolds. We show that locally it will behave in the same way, with the
same rate as predicted in [arXiv:1703.10547]. The goal is to get closer to a
rate for general convex sets, where convergence, but not rate is known. If a
finite identification property can be shown for two convex sets, to locally
smooth manifolds, then the rates from this paper also apply to those sets. We
present a few examples where this is the case, and also a counter example for
when this is not the case.
