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manuscripta mathematica

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

Osserman manifolds of dimension 8

  • Y. NikolayevskyEmail author
Article

Abstract.

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.

Keywords

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

Authors and Affiliations

  1. 1.Department of MathematicsLa Trobe UniversityBundooraAustralia

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