Volume 17, issue 1 (2013)

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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