Periodic flats and group actions on locally symmetric spaces

Abstract

We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension $\ge 3$, no metric $g$ has more symmetry than the locally symmetric metric. We also show that if $g$ is a finite volume metric that is not locally symmetric, then its lift to the universal cover has discrete isometry group.

12 pages

References in corpus (2)

• Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume
• The intrinsic asymmetry and inhomogeneity of Teichmuller space