#### Volume 17, issue 1 (2013)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Periodic flats and group actions on locally symmetric spaces

### Grigori Avramidi

Geometry & Topology 17 (2013) 311–327
##### Abstract

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

##### Keywords
aspherical manifolds, locally symmetric spaces, discontinuous transformation groups, smith theory
##### Mathematical Subject Classification 2010
Primary: 57S15, 57S20