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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

Syllabus

Main references

  • Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications

Recommended reading

  1. S. Kobayashi, “曲線と曲面の微分幾何（改訂版）” (in Japanese), Shokabo
  2. M. Umehara and K. Yamada, “曲線と曲面（改訂版）” (in Japanese), Shokabo

Course contents

  1. Parametrized differentiable curves
  2. Exercises
  3. Regular curves; arc length
  4. Exercises
  5. Curvature of curves
  6. Exercises
  7. Torsion of curves; the Frenet–Serret formulas
  8. Exercises
  9. The fundamental theorem of space curves
  10. Exercises
  11. The Jordan curve theorem; the rotation index theorem
  12. Exercises
  13. The four-vertex theorem
  14. Exercises
  15. The isoperimetric problem; the inscribed rectangle problem
  16. End-of-term exam and summary