Differential Geometry II

Differential geometry is the study of Riemannian manifolds and their local and global properties.

In this course, we will cover some topics in differential geometry, possibly including:

• Calculus of variations and Morse theory on the space of paths
• The Cartan-Hadamard theorem and the geometry of nonpositively curved manifolds
• The geometry of Lie groups and symmetric spaces
• Comparison geometry

Basic information

• Instructor: Robert Young (ryoung@cims.nyu.edu)
• Office: CIWW 601
• Office hours: Tuesdays, 1--2 or by appointment
• Lectures: CIWW 201, Thursdays, 1:25--3:15
• Sources:
  • Milnor, Morse theory
  • Lee, Riemannian Manifolds: An Introduction to Curvature (Springer)
  • Bridson and Haefliger, Metric Spaces of Non-Positive Curvature
  • Cheeger and Ebin, Comparison Theorems in Riemannian Geometry

Problem Sets

• Problem Set 1 (due Feb. 9) (2017-02-06: corrected some typos)
• Problem Set 2 (due Feb. 23) (2017-02-23: corrected a typo in question 2 (extra 2 in the denominator))
• Problem Set 3 (due Mar. 2)
• Problem Set 4 (due Mar. 23)
• Problem Set 5 (due Apr. 13) (2017-04-12: minor corrections)
• Problem Set 6 (due Apr. 27)