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Locally conformal flat Riemannian manifolds with constant principal Ricci curvatures and locally conformal flat C-spaces

Stefan Ivanov·Irina Petrova
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Abstract

It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given in dimensions 4,5,6,7 and 8. It is shown that any n-dimensional $(4\leq n \leq 8)$ locally conformal flat Riemannian manifold with constant principal Ricci curvatures is a Riemannian locally symmetric space.

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Stefan Ivanov, Irina Petrova. 1997-02-11. Locally conformal flat Riemannian manifolds with constant principal Ricci curvatures and locally conformal flat C-spaces. https://arxiv.org/abs/dg-ga/9702009

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