Math 547: Geometric Structures
Autumn Quarter: Riemannian Manifolds
Daniel Pollack
Autumn 1998, MWF 1:30-2:20
PREREQUISITES:
Topology and Geometry of Manifolds
(Math 544/5/6).
The first quarter of this 3 quarter sequence will be an introduction to the fundamentals of Riemannian geometry.
Definitions and examples of Riemannian metrics
Connections
Geodesics and distance
Curvature
Riemannian submanifolds and the Gauss-Bonnet theorem
Jacobi fields, and applications to curvature and topology
TEXTS:
Riemannian manifolds: An introduction to curvature
by John M. Lee
(Springer-Verlag GTM #176)