## Geometry & Topology

### Periodic flats and group actions on locally symmetric spaces

Grigori Avramidi

#### Abstract

We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension $≥3$, 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.

#### Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 311-327.

Dates
Revised: 10 October 2012
Accepted: 7 November 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732525

Digital Object Identifier
doi:10.2140/gt.2013.17.311

Mathematical Reviews number (MathSciNet)
MR3035329

Zentralblatt MATH identifier
1272.57026

#### Citation

Avramidi, Grigori. Periodic flats and group actions on locally symmetric spaces. Geom. Topol. 17 (2013), no. 1, 311--327. doi:10.2140/gt.2013.17.311. https://projecteuclid.org/euclid.gt/1513732525

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