Conformally flat Einstein-like 4-manifolds and conformally flat Riemannian 4-manifolds all of whose Jacobi operators have parallel eigenspaces along every geodesic
نویسندگان
چکیده
A local classification of all locally conformal flat Riemannian 4-manifolds whose Ricci tensor satisfies the equation ∇ ( ρ− 1 6 sg ) = 1 18 ds⊙ g as well as a local classification of all locally conformal flat Riemannian 4-manifolds for which all Jacobi operators have parallel eigenspaces along every geodesic is given. Non-trivial explicit examples are presented. The problem of local description of self-dual Einstein-like 4-manifolds is also treated. A complete explicit solution of the Stäckel system in dimension 4 is obtained. Running title: Einstein-like 4-manifolds
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