Conformally flat manifolds and a pinching problem on the Ricci tensor
Conformally flat manifolds and a pinching problem on the Ricci tensor
There is a formal similarity between the theory of hypersurfaces and conformally flat ^-dimensional spaces of constant scalar curvature provided d > 3. For, then, the symmetric linear transformation field Q defined by the Ricci tensor satisfies Codazzi's equation (VXQ)Y = (VYQ)X.This observation leads to a pinching theorem on the …