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

Manifold 

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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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