  The local convergence of an inexact Newton method is studied for solving
generalized equations on Riemannian manifolds by using the metric regularity
property which is explored as well. Under suitable conditions and without any
additional geometric assumptions, local convergence results with linear and
quadratic rate and a semi-local convergence result are obtained for the
proposed method. Finally, the theory can be applied to problems of finding a
singularity of the sum of two vector fields.
