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SymmetricSpaceRules

SymmetricSpaceRules[cd, K]
produces replacement rules for the curvature tensors of the covariant derivative cd on a symmetric space of constant curvature K.
  • On a symmetric space of constant curvature K, the Riemann tensor takes the value R_(abcd)=K(g_(ac)g_(bd)-g_(ad)g_(bc)) .
  • SymmetricSpaceRules gives replacement rules for the Riemann, Weyl, Ricci, tracefree Ricci, (cosmological) Einstein, (cosmological) Schouten tensors, and the Ricci and Kretschmann scalars.