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

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

1997-02-11

arxiv.org/abs/dg-ga/9702009v1

Mathematics

Differential Geometry

10 pages, Latex format, no figers

Scientific paper

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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