Osserman Conjecture in dimension n \ne 8, 16

Details Osserman Conjecture in dimension n \ne 8, 16 Osserman Conjecture in dimension n \ne 8, 16

2002-04-22

arxiv.org/abs/math/0204258v2

Mathematics

Differential Geometry

16 pages, LATeX file, changed content

Scientific paper

Let M be a Riemannian manifold and R its curvature tensor. For a unit vector X tangent to M at a point p, the Jacobi operator is defined by R_X = R(X, .) X$. The manifold M is called pointwise Osserman if, for every point p, 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. R.Osserman conjectured that globally Osserman manifolds are two-point homogeneous. We prove the Osserman Conjecture for dimension n \ne 8, 16, and its pointwise version for n \ne 2,4,8,16. Partial results in the cases n = 8, 16 are also given.

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