Differential Geometry II

Department: 
MATH
Course Number: 
6456
Hours - Lecture: 
3
Hours - Total Credit: 
3
Typical Scheduling: 
Some spring semesters

This course deepens the understanding of several topics covered in 6455 and introduces new concepts in at least one area foundational to modern differential geometry.

Prerequisites: 

Math 6455, or permission of the instructor

Course Text: 

See syllabus; text will vary by topic coverage

Topic Outline: 

Topics covered will fall into one or more of the following areas: 

 

  • 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)