Differential Geometry
גיאומטריה דיפרנציאלית
Fall semester 2024/25
- Lecturer: Bo'az Klartag
Teaching assistant: Matan Eilat
- Classes: Wednesday, 14:15 - 17:00, Ziskind 155
The semester begins on November 3, 2024 and ends on January 31, 2025.
There will be no class on November 20.
The class on November 27 will take place in Goldschmidt 108, and not in Ziskind.
- Mailing list: Please fill this form in order to join the course mailing list. Students that plan to submit their homework must join the mailing list.
- Syllabus
This course consists of two parts.
The first part is "Analysis on Manifolds", starting from the definition a differentiable manifold, vectors fields, differential forms, integration, Stokes theorem.
The second part is "Curvature" and it focuses on Riemannian manifolds and submanifolds of Euclidean space. Time permitting, we will cover topics such as the Riemannian metric, parallel transport, connections, geodesics and curvature.
- Prerequisites
Familiarity with multivariate calculus (say, the divergence threorem) and point-set topology (say, a Hausdorff topological space).
- Final grade
It will be based on the solution of the homework exercises.
- Related literature
- Lee, J. M, Introduction to Smooth Manifolds, 2003.
- Hitchin's notes on Differentiable Manifolds, 2014.
- DoCarmo, Riemannian Geometry, 1992.
- Chavel, Riemannian geometry - a modern introduction, 1994.
- A short appendix by Gromov, "Isoperimetric Inequalities in Riemannian Manifolds" in the book by Milman and Schechtman, "Asymptotic Theory of Finite Dimensional Normed Spaces", 2001.
- Singer and Thorpe, Lecture Notes on Elementary Topology and Geometry, 1967 (Our presentation of 2D Riemannian geometry follows chapter 7)
- Homework assigments