OAI/Geometry/SurfaceImmersion/Whitney/CrosscapAxisCurve.lean

GitHub source file

6 declarations, 0 contain sorry, 0 declared as axioms

The kernel axis of an actual crosscap chart gives a smooth regular source curve through the singular point, even though its image velocity vanishes.

  1. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapAxis line 13
  2. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapAxis_apply line 16
  3. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapAxis_injective line 20
  4. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapAxis_regular line 24
  5. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SurfaceCrosscapCoordinates.axisCurve line 34
  6. theorem OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SurfaceCrosscapCoordinates.axis_curve line 36