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Abstract: A Riemannian manifold is called Osserman conformally Osserman,respectively, if the eigenvalues of the Jacobi operator of its curvaturetensor Weyl tensor, respectively are constant on the unit tangent sphere atevery point. Osserman Conjecture asserts that every Osserman manifold is eitherflat or rank-one symmetric. We prove that both the Osserman Conjecture and itsconformal version, the Conformal Osserman Conjecture, are true, modulo acertain assumption on algebraic curvature tensors in $\mathbb{R}^16$. As aconsequence, we show that a Riemannian manifold having the same Weyl tensor asa rank-one symmetric space, is conformally equivalent to it.



Author: Y. Nikolayevsky

Source: https://arxiv.org/







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