Geometry & Topology

Periodic flats and group actions on locally symmetric spaces

Grigori Avramidi

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

Permanent link to this document
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

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

Keywords
aspherical manifolds locally symmetric spaces discontinuous transformation groups smith theory

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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