CurvatureRelations

• CurvatureRelations is a Boolean option for DefCovD specifying whether contractions of the Riemann tensor must be replaced by the Ricci tensor, and (if there is a metric) contractions of the Ricci tensor must be replaced by the RicciScalar tensor.
• CurvatureRelations[covd, Riemann] returns the list of rules converting the contractions of the Riemann tensor of covd into its Ricci tensor.
• CurvatureRelations[covd, Ricci] returns the list of rules converting the contractions of the Ricci tensor of covd into its RicciScalar.
• CurvatureRelations[covd] returns the list of rules converting the contractions of the Riemann and Ricci tensors of covd into Ricci and RicciScalar, respectively.
• CurvatureRelations[] returns all rules for those contractions of all derivatives.

• The default value for the option is True.
• All those rules are used by the function ContractCurvature.
• See: Section 4.5.
• See also: DefCovD.
• New in version 0.
• Last update: 15-X-2007 for version 0.9.3 of xTensor`.

Created by Mathematica  (May 16, 2008)