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Pré-Publication, Document De Travail Année : 2023

Local rigidity of actions of isometries on compact real analytic Riemannian manifolds

Résumé

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.

Dates et versions

hal-04399082 , version 1 (17-01-2024)

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Laurent Stolovitch, Zhiyan Zhao. Local rigidity of actions of isometries on compact real analytic Riemannian manifolds. 2024. ⟨hal-04399082⟩
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