Math 140: Differential Geometry

UC Berkeley, Spring 2019


Michael Hutchings
Office: 923 Evans.
Tentative office hours: Thursday 9:00-11:00


You can ask questions and have discussions at the piazza site here.



This course is about the geometry of curves and surfaces in three-dimensional space. We will also study the "intrinsic" geometry of surfaces: that is, geometric notions which are described just in terms of the surface and not in terms of an embedding of the surface into three- or higher-dimensional space. A central theme is to study different kinds of curvature - defined locally on a curve (in chapter 2 of the book) or surface (in chapter 4) - and how curvature relates to global properties of the curve or surface (in chapters 3, 5, and 6). One of the main results in this direction which we will prove near the end of the course is the Gauss-Bonnet theorem, and we will also see several others. If time permits we will give an introduction on how to generalize differential geometry from curves and surfaces to spaces (manifolds) of any dimension (chapter 7).



Homework assignments will be due on Tuesdays at the beginning of class. Note: To get full credit, please write clear solutions using complete English sentences (with mathematical symbols inserted as appropriate). You are welcome to collaborate or look things up, but you must write your own solutions and cite any sources or collaborators.

Lecture summaries and references

After each lecture, summaries and reading suggestions will be posted here.