Conformally Osserman manifolds

Details Conformally Osserman manifolds Conformally Osserman manifolds

2008-10-31

arxiv.org/abs/0810.5621v1

Mathematics

Differential Geometry

23 pages

Scientific paper

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension $n \ne 3, 4, 16$ is locally conformally equivalent either to a Euclidean space or to a rank-one symmetric space.

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