OAI/Geometry/EinsteinFour/FrameOrientation.lean

GitHub source file

10 declarations, 0 contain sorry, 0 declared as axioms

An orientation is a continuous choice of one of the two orientation classes in every orthonormal frame fiber. This separates the individual Weyl norms used by the scalar argument from the orientation-independent sum used in radial averaging.

  1. structure OAI.PositiveEinsteinFour.Geometry.FrameOrientation line 20

    Also declared: ComparatorChallenges/EinsteinFour.lean:139 (same declaration text).

  2. def OAI.PositiveEinsteinFour.Geometry.FrameOrientation.frame line 28
  3. theorem OAI.PositiveEinsteinFour.Geometry.FrameOrientation.frame_positive line 31
  4. theorem OAI.PositiveEinsteinFour.Geometry.FrameOrientation.positive_iff_det line 35
  5. def OAI.PositiveEinsteinFour.Geometry.plusNorm line 40
  6. def OAI.PositiveEinsteinFour.Geometry.minusNorm line 43
  7. theorem OAI.PositiveEinsteinFour.Geometry.plusNorm_nonneg line 46
  8. theorem OAI.PositiveEinsteinFour.Geometry.minusNorm_nonneg line 49
  9. theorem OAI.PositiveEinsteinFour.Geometry.plusNorm_eq_zero_iff line 52
  10. theorem OAI.PositiveEinsteinFour.Geometry.minusNorm_eq_zero_iff line 56