Osserman Conjecture in dimension n ≠ 8, 16

2002/04/22 by Y. Nikolayevsky, Nikolayevsky, Y.
Mathematics · #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C25

paper · pdf · doi:10.48550/arxiv.math/0204258

16 pages, LATeX file, changed content

arxiv created 2002/10/10 · arxiv updated 2009/11/30

Abstract

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 ≠ 8, 16, and its pointwise version for n ≠ 2,4,8,16. Partial results in the cases n = 8, 16 are also given.

Related

• Osserman manifolds of dimension 8
• Osserman manifolds and Weyl-Schouten Theorem for rank-one symmetric spaces
• Conformally Osserman manifolds
• The Orthogonality Principle for Osserman Manifolds
• Projectively Osserman manifolds