Math 645: Riemannian Geometry
This is a graduate level introduction to Riemannian geometry. Some basic familiarity with the theory of differential manifolds will be assumed, though there will be some review in the first two weeks. The course will follow Gallot, Hulin and Lafontaine's "Riemannian Geometry" with some omissions and some supplementary material. There will be about 10 problem sets and no exams.
The course meets Tuesday and Thursday 10:30-11:45 in Krieger 111.
Problem sets will be due in class on Thursdays (see below for dates).
Office Hours: Tuesday 1:30-3:30pm or by appointment, in Krieger 408.
ReferencesThe course text is
Week 1: Smooth Manifolds.
Week 2: Smooth Manifolds.
Week 3: Smooth Manifolds.
Week 4: Riemannian Metrics, Connections.
Week 5: Connections, Geodesics.
Week 6: Geodesics.
Week 7: Curvature.
Week 8: Curvature
Week 9: Curvature.
Week 10: Analysis on Manifolds.
Week 11: Analysis on Manifolds.
Week 12: THANKSGIVING
Week 13: Submanifold Theory.
Week 14: Submanifold Theory.