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, Volume 93, Issue 1, pp 205–217 | Cite as

On space forms of Grassmann manifolds

  • Brett McInnes


We show that, in each odd dimensionn =m 2, there is a class of Grassmann quotient spaces not included in Wolf’s classic solution of the Grassmann space form problem. We classify all of these new Grassmann space forms up to isometry. As an application, we exhibit a pair of compact Einstein manifolds of dimensionm 2 with holonomy groups which are abstractly isomorphic yet not conjugate in the orthogonal group, thus proving that a theorem of Besse cannot be extended to non-simply-connected Einstein manifolds.


Riemannian Manifold Symmetric Space Space Form Maximal Torus Einstein Manifold 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Brett McInnes
    • 1
  1. 1.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore

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