Geometry & Topology

Periodic flats and group actions on locally symmetric spaces

Grigori Avramidi

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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

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

Received: 1 August 2011
Revised: 10 October 2012
Accepted: 7 November 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57S15: Compact Lie groups of differentiable transformations 57S20: Noncompact Lie groups of transformations

aspherical manifolds locally symmetric spaces discontinuous transformation groups smith theory


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.

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