  We establish the Krylov Safonov Harnack inequalities and Holder estimates for
fully nonlinear nonlocal operators of non-divergence form on Riemannian
manifolds with nonnegative sectional curvatures. To this end, we first define
the nonlocal Pucci operators on manifolds that give rise to the concept of
non-divergence form operators. We then provide the uniform regularity results
for these operators which recover the classical results for second order local
operators as limits.
