Conformally flat Einstein-like 4-manifolds and conformally flat Riemannian 4-manifolds all of whose Jacobi operators have parallel eigenspaces along every geodesic

Details Conformally flat Einstein-like 4-manifolds and conformally flat Riemannian 4-manifolds all of whose Jacobi operators have parallel eigenspaces along every geodesic Conformally flat Einstein-like 4-manifolds and conformally flat Riemannian 4-manifolds all of whose Jacobi operators have parallel eigenspaces along every geodesic

1997-02-24

arxiv.org/abs/dg-ga/9702019v1

Mathematics

Differential Geometry

24 pages, LaTex, no figures

Scientific paper

A local classification of locally conformal flat Riemannian Einstein-like four-manifolds as well as a local classification of all locally conformal flat Riemannian four-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 four-manifolds is also treated. A complete explicit solution of the St\"ackel system in dimension four is obtained.

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