Messages
I have added Lemma 1.6.1, revised the proof of Proposition 1.6.1, and added Sections 2.4 and 2.5.
The assignment problems will be posted no later than the 17th October and the solutions should be returned through Canvas by the 31st October.
I have added Sections 2.1 and 2.2, some material at the end of Section 1.6, and definitions of "codimension" and "hypersurface" on page 7.
I have made minor corrections in the previously published material and added Section 1.6 and Problem 1.9.
I am very sorry that I have had to cancel this week's lectures, but I do expect to be back on Tuesday next week. Meanwhile, you can take a look at the first sections of the lecture notes.
The first chapter of the lecture notes is now available. The notes will be expanded throughout the semester.
The course will be based on a new set of lecture notes extending those from last year (with some changes). The first few sections will be available before the semester begins. Here is the plan for the course:
Chapter 1. Manifolds, tangent spaces, smooth maps
Chapter 2. Classical surface theory: First and second fundamental forms, Gauss curvature
Chapter 3. Intrinsic geometry: Covariant derivatives and curvature, geodesics, the exponential map
Chapter 4. Hyperbolic Geometry: Four models for the hyperbolic plane, geodesics, isometry groups, hyperbolic trigonometry.
Chapter 5. The Gauss-Bonnet theorem.
The choice of material is much influenced by the book
Christian B?r: "Elementary Differential Geometry".
However, we will prove the version of the Gauss-Bonnet theorem given in ...