  In this article, we consider analytic perturbations of isometries of an
analytic Riemannian manifold M. We prove that, under some conditions, a
finitely presented group of such small enough perturbations is analytically
conjugate on M to the same group of isometry it is a perturbation of. Our
result relies on a "Diophantine-like" condition, relating the actions of the
isometry group and the eigenvalues of the Laplace-Beltrami operator. Our result
generalizes Arnold-Herman's theorem about diffemorphisms of the circle that are
small perturbations of rotations.
