Periodic flats and group actions on locally symmetric spaces
  We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension $\geq 3$, 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. 
Grigori Avramidi
math.GT math.AT