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- W2056539557 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." @default.
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- W2056539557 date "2004-08-10" @default.
- W2056539557 modified "2023-09-30" @default.
- W2056539557 title "Osserman manifolds of dimension 8" @default.
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- W2056539557 doi "https://doi.org/10.1007/s00229-004-0480-y" @default.
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