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Mathematische Annalen

, Volume 331, Issue 3, pp 505–522 | Cite as

Osserman Conjecture in dimension n ≠ 8, 16

  • Y. NikolayevskyEmail author
Article

Abstract.

Let M n be a Riemannian manifold and R its curvature tensor. For a point pM n and a unit vector XT p M n , the Jacobi operator is defined by R X =R(X,·)X. The manifold M n is called pointwise Osserman if, for every pM n , the spectrum of the Jacobi operator does not depend of the choice of X, and is called globally Osserman if it depends neither of X, nor of p. Osserman conjectured that globally Osserman manifolds are two-point homogeneous. We prove the Osserman Conjecture for n≠8, 16, and its pointwise version for n≠2, 4, 8, 16. Partial result in the case n=16 is also given.

Keywords

Manifold Unit Vector Riemannian Manifold Curvature Tensor Partial Result 
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 2005

Authors and Affiliations

  1. 1.Department of MathematicsLa Trobe UniversityBundooraAustralia

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