Math 530: Differential Geometry
Fall 2004 TR 1:00-2:15pm, 304 Willard

Instructor: Aissa Wade
Office: 02L Thomas Building
Phone: (814) 865-7311
Fax: (814) 865-3735
Office Hours (Fall 2004): M 4:00-5:00 and by appointment.

Textbook: Riemannian Manifold: An Introduction to Curvature, by John M. Lee, Springer, 1997.  

Recommended reading:
Riemannian Geometry by Do Carmo

Prerequisites: Be familiar with differentiable manifolds, differential forms.

This course is intended to introduce fundamental concepts and tools of differential geometry with a special emphasis on Riemannian manifolds. Topics include

  • Distributions and Frobenius Theorem
  • Principal bundles - Vector bundles
  • Riemannian Metrics
  • Model Spaces of Riemannian Geometry
  • Connections. Riemannian Connections
  • Geodesics
  • The Exponential Map
  • Completeness
  • Curvature. Ricci and Scalar Curvatures
  • Gauss-Bonnet Theorem
  • Jacobi Fields
  • Curvature and Topology