Conformally Flat Semi-Riemannian Manifolds with Nilpotent Ricci Operators and Affine Differential Geometry

摘要

We investigate the conformally flat semi-Riemannian manifolds with nilpotent Ricci operators. We construct a lot of complete or homogeneous, conformally flat semi-Riemannian manifolds with nilpotent Ricci operators. In this construction, we show interesting relations between the semi-Riemannian geometry and the affine differential geometry of centro-affine hypersurfaces.