OAI/Geometry/SurfaceImmersion/Atlas/NonparallelPhaseCovectors.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Two independently perturbed phase covectors can avoid parallelism in every open parameter set. Only the two-dimensional determinant is used.

  1. def OAI.ClosedSurfaceR4.PhaseGeometry.covectorDet line 14
  2. def OAI.ClosedSurfaceR4.PhaseGeometry.covectorDetMap line 16
  3. lemma OAI.ClosedSurfaceR4.PhaseGeometry.covectorDetMap_apply line 19
  4. lemma OAI.ClosedSurfaceR4.PhaseGeometry.covectorDetMap_surjective line 21
  5. lemma OAI.ClosedSurfaceR4.PhaseGeometry.dense_nonzero_covectors line 37
  6. lemma OAI.ClosedSurfaceR4.PhaseGeometry.covectorDet_open_dense line 42