Schouten tensor

In Riemannian geometry the Schouten tensor is a second-order tensor introduced by Jan Arnoldus Schouten defined for n ≥ 3 by: where Ric is the Ricci tensor (defined by contracting the first and third indices of the Riemann tensor), R is the scalar curvature, g is the Riemannian metric,

In an index notation The Schouten tensor often appears in conformal geometry because of its relatively simple conformal transformation law where

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