Announcements
- This differential geometry course meets first on Thursday 9/3/2026. See the Fas Fall Calendar
- We meet Thursday 12:00pm - 1:15pm in Hall E.
- OH: tentative MWF (probably 11-12)
- An introduction Riemannian geometry and especially curves and surfaces in space where the fundamental notions can be visualized.
- Prerequisites are 19a,b or 21a,b or 22a,b or 23a or 25a or 55a or an equivalent background in mathematics.
- Grades: Grades: HW 40 percent, midterm 30 (inclass and take home combined), final 30 (inclass and paper combined)
Lecture plan:
W1 1 Tuesday September 3th: What is differential geometry
W2
2 Tuesday September 8: Parametrized and implicit surfaces
3 Tuesday September 10: Surface area, arc length
W3
4 Thursday September 15: The Frenet theorem in two and 3 dimensions
W3 5 Tuesday September 17: The Frenet theorem in arbitrary dimensions
W4 6 Tuesday September 22: A global result: The Hopf Umlaufsatz
7 Thursday September 24: A global result: The four vertex theorem
W5 8 Tuesday September 19: The fundamental forms I,II,III
9 Thursday October 1: The Gauss Map A and Curvature K
W6 10 Tuesday October 6: Euler characteristics
11 Thursday October 8: Discrete Differential geometry
W7 12 Tuesday October 13: Review for midterm
13 Thursday October 15: Inclass part Midterm
W8 14 Tuesday October 20: Calculus of variations and Geodesics
15 Thursday October 22: Exponential map and geodesic coordinates
W9 16 Tuesday October 27: Differential forms and Green's Theorem
17 Thursday October 29: The Theorema Egregium
W10 18 Tuesday November 3: Local Gauss Bonnet theorem
19 Thursday November 5: Global Gauss Bonnet theorem
W11 20 Tuesday November 10: Riemannian manifolds
21 Thursday November 12: Discrete manifolds
W12 22 Tuesday November 17: The curvature and Ricci tensors
23 Thursday Novemer 19: General relativity
W13 24 Tuesday November 24:
November 25 until November 29 Thanksgiving
W14 25 Tuesday December 1: Final review
26 Thursday December 3: In class part final
