Osserman manifolds of dimension 8
نویسنده
چکیده
For a Riemannian manifold M n with the curvature tensor R, the Jacobi operator RX is defined by RX 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 RX do not depend of a unit vector X ∈ TpM 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 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.
منابع مشابه
ct 2 00 2 Osserman Conjecture in dimension n 6 = 8 , 16
Let M n be a Riemannian manifold and R its curvature tensor. For a point p ∈ M n and a unit vector X ∈ TpM n , the Jacobi operator is defined by RX = R(X, ·)X. The manifold M n is called pointwise Osserman if, for every p ∈ M 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...
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