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Ryuma ORITA
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Geometry IA

Term 1, Mon. Period 3 & Thu. Period 2 · Faculty of Science, Niigata University

Note

This course is held online via Zoom.

References

Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces, Dover Publications

Course contents

  1. Parametrized differentiable curves; inner products (04-20)
  2. Exercises; quiz 1 (04-23)
  3. Regular curves; arc length; orientation of vector spaces; cross products (04-27)
  4. Exercises; quiz 2 (04-30)
  5. Properties of the cross product; curvature of curves; principal normal vectors (05-04)
  6. Exercises; quiz 3 (05-07)
  7. Binormal vectors; torsion; the Frenet–Serret formulas; radius of curvature (05-11)
  8. Exercises; quiz 4 (05-14)
  9. The fundamental theorem of space curves; local canonical form (05-18)
  10. Exercises; quiz 5 (05-21)
  11. The Jordan curve theorem; the rotation index of plane curves (05-25)
  12. Exercises; quiz 6 (05-28)
  13. The rotation index theorem; the four-vertex theorem (06-01)
  14. Exercises; quiz 7 (06-04)
  15. Proof of the four-vertex theorem (06-08)
  16. Exercises; quiz 8 (06-11)