Instructor. Michael Anderson, Math 4-110.
E-mail: anderson@math.sunysb.edu, Phone: 632-8269.
Lectures: Tu/Th: 2:30-3:50, in ESS 183.

Office Hours. TBA

Course Description. This semester course will cover basic issues in Riemannian geometry: metrics, geodesics, covariant derivatives (connections) and curvature, leading to the fundamental theorems of Cartan-Hadamard and Bonnet-Myers. Both modern conceptual and computational aspects (examples) will be emphasized and related to each other, i.e. no blind or brute force computation.

The syllabus is most of the main topics in Chapters 1-6 of Petersen's text. The presentation of this material in the lectures will often be quite different than that in the text.

Prerequistes MAT 530 and 531, or the equivalent.

Main Text. Peter Petersen, Riemannian Geometry, 2nd Edition, Springer Verlag.
You will not need to have this text for the course, but having it will be very useful. It is the only "modern" text in Riemannian geometry really out there.

There are some other good texts on this subject. Some other sources you might like to look at are:

• M. doCarmo, Riemannian Geometry
• M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. I, II, Publish or Perish,
• S. Gallot, D. Hulin and J. Lafontaine, Geometrie Riemannienne, (in French)
• D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geometrie im Grossen (in German)
• J. Jost, Riemannian Geometry and Geometric Analysis
• John M. Lee, Intro to Riemannian Manifolds, Springer Verlag

Assignments and Grading. Grades will be based on class participation and occassional homework assignments.

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