Special Math Lecture： Differential geometry

Aim of the course

Differential geometry plays a central role in many physical theory, as for example in classical mechanics, in solid states physics or in general relativity. During this one semester course, many essential notions will be introduced, among them the definitions of a manifold, of the curvature, of the parallel transport, of the holonomy, etc. Depending on the interest of the audience, applications in one of the mentioned theory will be proposed.

Course Prerequisites

Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II. Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.

Course Content

I) Differentiable manifolds
II) Tensors, tensor fields and differential forms
III) Integration on manifolds
IV) Riemannian manifolds:
V) Curvature
VI) General relativity

Course Evaluation Methods

The final grade will be determined by the active participation during the lectures (as explained during the first lecture).

Notice for Students

This course is an optional subject which does not count towards the number of credits required for graduation in any program at Nagoya University.

Textbook

Material will be provided during the lectures

Reference Book

See the website

Lecture Notes

Differential geometry notes

---