Jacob Bernstein






Math 645: Riemannian Geometry

Course Description

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.


The course text is
  • S. Gallot, D. Hulin and J. Lafontaine, "Riemannian Geometry," 3rd Ed.
Some other resources are
  • M. Do Carmo, ‚ÄúRiemannian Geometry".
  • F. W. Warner, "Foundations of Differential Manifolds and Lie Groups";
  • W. Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry";
  • P. Petersen, "Riemannian Geometry";
  • J. Jost, "Riemannian Geometry and Geometric Analysis";
  • I. Chavel, "Riemannian Geometry: A Modern Introduction".

(Tentative) Schedule

Week 1: Smooth Manifolds.

No problem set due.

Week 2: Smooth Manifolds.

No problem set due.

Week 3: Smooth Manifolds.

Problem set 1 due.

Week 4: Riemannian Metrics, Connections.

Problem set 2 due.

Week 5: Connections, Geodesics.

Problem set 3 due.

Week 6: Geodesics.

Problem set 4 due.

Week 7: Curvature.

Problem set 5 due.

Week 8: Curvature

Problem set 6 due.

Week 9: Curvature.

Problem set 7 due.

Week 10: Analysis on Manifolds.

No problem set due.

Week 11: Analysis on Manifolds.

Problem set 8 due. (On Tuesday).


No Problem set due.

Week 13: Submanifold Theory.

No problem set due.

Week 14: Submanifold Theory.

Problem set 9 due.

Fall 2017 -- Department of Mathematics, Johns Hopkins University.