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Rigidity of lattices of non-positive curvature

Published online by Cambridge University Press:  19 September 2008

P. Eberlein
P. Eberlein
Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27514
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Abstract

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Let M, M* denote compact, connected manifolds of non-positive sectional curvature whose fundamental groups are isomorphic and whose Euclidean de Rham factors are trivial. We prove that: if M is a compact irreducible quotient of a reducible symmetric space H, then M and M* are isometric up to a constant multiple of the metric; and that the number and dimensions of the local de Rham factors are the same for M and M*. Gromov has independently proved the first result in the more general case that M is locally symmetric and globally irreducible with rank at least two.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 1 , March 1983 , pp. 47 - 85
Copyright
Copyright © Cambridge University Press 1983

References

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