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Ryuma ORITA
  1. Teaching/

Geometry IIA

Term 3, Mon. Period 3 · Faculty of Science, Niigata University

Syllabus

Note

This course is held online via Zoom.

Textbooks

  1. Y. Matsumoto, “多様体の基礎” (in Japanese), University of Tokyo Press

Main references

  1. L. W. Tu, “An Introduction to Manifolds” (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo)

Course contents

  1. Definition of manifolds
  2. Examples of manifolds
  3. $C^s$ functions and $C^s$ maps
  4. $C^s$ diffeomorphisms; directional derivatives
  5. Tangent spaces
  6. Differentials of $C^r$ maps, part 1
  7. Differentials of $C^r$ maps, part 2
  8. Local properties of maps