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Mostow’s rigidity theorem and its generalization. An outline of the proof

  • Werner Ballmann
  • Mikhael Gromov
  • Viktor Schroeder
Part of the Progress in Mathematics book series (PM, volume 61)

Abstract

Let V* and V be compact locally symmetric spaces of nonpositive curvature with isomorphic fundamental group. Hence V* = X*/Γ*, V = X/Γ, where X* and X are symmetric spaces and Γ* is isomorphic to Γ. Let us assume that in the de Rham decomposition of X* and X there are no Euclidean factors and no factors isometric to the hyperbolic plane, then by the famous rigidity theorem of [Mostow, 1973], V* and V are isometric up to normalizing constants. Thus, if the metric of X is multiplied on each de Rham factor by a suitable constant, then X*/Γ* and X/Γ are isometric.

Keywords

Riemannian Manifold Symmetric Space Fundamental Group Hyperbolic Plane Nonpositive Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Werner Ballmann
    • 1
    • 2
  • Mikhael Gromov
    • 3
  • Viktor Schroeder
    • 4
    • 5
  1. 1.Dept. of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Math. Institut der UniversitätBonnWest Germany
  3. 3.Inst. des Hautes Etudes ScientifiquesBures-sur-YvetteFrance
  4. 4.Math. Institut der UniversitätMünsterGermany
  5. 5.Math. Institut der UniversitätBaselSwitzerland

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