Periodic flats and group actions on locally symmetric spaces

Avramidi, Grigori¹

¹ Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA

Geometry & topology, Tome 17 (2013) no. 1, pp. 311-327.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.311

Classification : 57S15, 57S20
Keywords: aspherical manifolds, locally symmetric spaces, discontinuous transformation groups, smith theory

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