↓ Skip to main content
Ryuma ORITA
  1. Teaching/

Geometry IIB

Term 4, Mon. Period 3 · 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. $C^{\infty}$ functions on surfaces
  2. $C^{\infty}$ maps between surfaces
  3. Tangent planes and differentials
  4. The first fundamental form, part 1 (definition, examples, lengths of curves on surfaces)
  5. The first fundamental form, part 2 (loxodromes, areas of regions on surfaces)
  6. The Gauss map; the second fundamental form
  7. Gaussian curvature; the Gauss–Bonnet theorem
  8. End-of-term exam