  This article develops nonparametric inference procedures for estimation and
testing problems for means on manifolds. A central limit theorem for Frechet
sample means is derived leading to an asymptotic distribution theory of
intrinsic sample means on Riemannian manifolds. Central limit theorems are also
obtained for extrinsic sample means w.r.t. an arbitrary embedding of a
differentiable manifold in a Euclidean space. Bootstrap methods particularly
suitable for these problems are presented. Applications are given to
distributions on the sphere S^d (directional spaces), real projective space
RP^{N-1} (axial spaces), complex projective space CP^{k-2} (planar shape
spaces) w.r.t. Veronese-Whitney embeddings and a three-dimensional shape space
\Sigma_3^4.
