Conformally Osserman manifolds

Yuri Nikolayevsky

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arXiv · 0810.5621

Conformally Osserman manifolds

Yuri Nikolayevsky

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Abstract

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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Yuri Nikolayevsky. 2008-10-31. Conformally Osserman manifolds. https://arxiv.org/abs/0810.5621

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