Math 2800: Differential Geometry 1

Syllabus

Office hours

Wed 2-3, Th 1-2, or by appointment (email me), in Thackeray 407

Text

Differential Geometry: Curves - Surfaces - Manifolds, by W. Kühnel

Homework

  • Assignment 1 (due Friday Sept. 5): Ch. 2, Exercises 2, 4, 7, 9, 11, 12.
  • Assignment 2 (due Friday Sept. 12): Ch. 2, Exercises 14-16, 18-20.
  • Assignment 3 (due Friday Sept. 19): Ch. 2, Exercises 13, 22-26.
  • Assignment 4 (due Friday Sept. 26)
  • Assignment 5 (due Friday Oct. 3): Ch. 3, Exercises 1, 3, 10, 17 and these.
  • Assignment 6 (due Friday Oct. 10 Tuesday Oct. 14): Ch. 3, Exercises 2, 4,
         5, 8, 11, and 12 (in 12, "in 3.26" should read "above 3.24").
  • Assignment 7 (due Friday Oct. 24): Ch. 3, Exercises 13-16, 20, 22, 23.
  • Assignment 8 (due Monday Nov. 10 Wednesday Nov. 12): Ch. 4, Exercises
         1, 2, 4, 5, and these.
  • Assignment 9 (due Wednesday Dec. 3) Ch. 4, Exercises 10, 16, 17, 20 - 23,
         and prove Lemma 4.17 for vector fields tangent to a hypersurface element.
         *This is the final homework assignment*

    • (Unless noted otherwise, problems are from the text.)

    Final Project

    Here is a list of some potential final topics (*working document*). Do not feel constrained by this list, but do consult with me about what you would like to do.

    Announcement

    On September 10 and thereafter, class will be held in Thackeray 427. Huzzah!

    NB: Kühnel's "slope line" is (seemingly) everyone else's "general helix".
    Jason's main page