Abstract
There is a formal similarity between the theory of hypersurfaces and conformally flat $d$-dimensional spaces of constant scalar curvature provided $d \geq 3$. For, then, the symmetric linear transformation field $Q$ defined by the Ricci tensor satisfies Codazziâs equation $({\nabla _X}Q)Y = ({\nabla _Y}Q)X$. This observation leads to a pinching theorem on the length of the Ricci tensor.
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