OAI/Geometry/EinsteinFour/CurvatureSecondBianchi.lean

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10 declarations, 0 contain sorry, 0 declared as axioms

The coordinate second Bianchi identity. The matrix algebra separates the commuting second derivatives from the Jacobi cancellation.

  1. abbrev OAI.PositiveEinsteinFour.CovariantBianchi.Mat line 16
  2. def OAI.PositiveEinsteinFour.CovariantBianchi.curvature line 18
  3. theorem OAI.PositiveEinsteinFour.CovariantBianchi.curvature_skew line 21
  4. def OAI.PositiveEinsteinFour.CovariantBianchi.curvatureDerivative line 26
  5. def OAI.PositiveEinsteinFour.CovariantBianchi.covariantCurvatureDerivative line 30
  6. theorem OAI.PositiveEinsteinFour.CovariantBianchi.cyclic_identity_of_commuting_derivatives line 34
  7. def OAI.PositiveEinsteinFour.CovariantBianchi.lowerSlotCorrection line 45
  8. theorem OAI.PositiveEinsteinFour.CovariantBianchi.lowerSlotCorrection_cyclic line 49
  9. def OAI.PositiveEinsteinFour.CovariantBianchi.tensorCurvatureDerivative line 62
  10. theorem OAI.PositiveEinsteinFour.CovariantBianchi.tensorCurvatureDerivative_cyclic line 66