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, Volume 115, Issue 1, pp 31–53 | Cite as

Osserman manifolds of dimension 8

  • Y. NikolayevskyEmail author


For a Riemannian manifold M n with the curvature tensor R, the Jacobi operator R X is defined by R X Y=R(X,Y)X. The manifold M n is called pointwise Osserman if, for every p ∈ M n , the eigenvalues of the Jacobi operator R X do not depend of a unit vector X ∈ T p M n , and is called globally Osserman if they do not depend of the point p either. R. Osserman conjectured that globally Osserman manifolds are flat or locally rank-one symmetric. This Conjecture is true for manifolds of dimension n≠8,16[14]. Here we prove the Osserman Conjecture and its pointwise version for 8-dimensional manifolds.


Unit Vector Riemannian Manifold Curvature Tensor Jacobi Operator Osserman Manifold 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsLa Trobe UniversityBundooraAustralia

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