Hidden symmetry and arithmetic manifolds
Differential Geometry
2007-05-23 v1 Geometric Topology
Abstract
A "hidden symmetry" of a Riemannian manifold M is an isometry of a d-sheeted, 1<d<\infty, 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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Cite
@article{arxiv.math/0405160,
title = {Hidden symmetry and arithmetic manifolds},
author = {Benson Farb and Shmuel Weinberger},
journal= {arXiv preprint arXiv:math/0405160},
year = {2007}
}
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13 pages