Hidden symmetry and arithmetic manifolds
Benson Farb, Shmuel Weinberger
Abstract
A "hidden symmetry" of a Riemannian manifold M is an isometry of a d-sheeted, 1<d<∞, Riemannian cover of M which is not the lift of any isometry. In this paper we characterize the locally symmetric metric(s) on a closed, arithmetic manifold as the unique metric with infinitely many hidden symmetries.
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