Hidden symmetry and arithmetic manifolds

2004/05/10 by Benson Farb, Shmuel Weinberger, Farb, Benson +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.math/0405160

13 pages

arxiv created 2004/05/10 · arxiv updated 2009/12/01

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.

Related

• Minimal orbifolds and (a)symmetry of piecewise locally symmetric manifolds
• Non-compact arithmetic manifolds have simple homotopy type
• Symmetry gaps in Riemannian geometry and minimal orbifolds
• Riemannian symmetries in flag manifolds
• The index of symmetry of compact naturally reductive spaces