Differential Geometry II

Department: 
MATH
Course Number: 
6456
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Not Regularly Scheduled

The course deepens the understanding of several topics covered in 6455 and introduces the new concepts foundational to modern differential geometry.

Prerequisites: 

Math 6455

Topic Outline: 

The course will cover topics in one or more of the following areas, as determined by the instructor: 

 

  • Comparison geometry (sectional and Ricci curvature comparison)
  • Metric geometry (Alexandrov spaces, CAT(k) spaces,  Gromov-Hausdorff convergence)
  • Geometric analysis (uniformization, curvature flows, isometric embeddings, isoperimetric inequalities, index theory, spectral geometry, Bochner technique)
  • Geometric structures on manifolds (projective, flat, affine, Thurston geometries, special holonomy)