Math 112: Riemannian Geometry

Winter 2013




Instructor Craig Sutton
Lectures MWF 1:45-2:50 (108 Kemeny)
X-Hour Tu 1-1:50 (108 Kemeny)
Office Hours Tu 5:30-6:30, Fri. 3:30-4:30 (also by appointment)
Office 321 Kemeny Hall
E-mail Craig.J.Sutton AT You Know Where
Phone 603-646-1059
Syllabus, Announcements, etc.

Homework Syllabus


Course Description: Manifolds are one way in which mathematicians deal with the concept of "space," and the presence of a Riemannian metric on a manifold provides us with a framework and a set of tools with which we may explore the geometric and topological nature of the space in question. Among the tools available to us, curvature is perhaps the most fundamental. The three primary flavors of curvature are sectional curvature, Ricci curvature and scalar curvature, and each provides us with a local characterization of how much a given space deviates from being Euclidean. After laying the basic foundations of Riemannian geometry, one of our main objectives will be to examine how (global) constraints on curvature influence the topological and geometric structure of the space.

Topics: connections, Riemannian metrics, volume, curvature and isometries; geodesics, Jacobi fields, the energy functional, first & second variations of energy; spaces of constant curvature; (locally) symmetric spaces; isoperimetirc inequalities; spectral geometry; sphere theorems.

Prerequisites: Math 124 or the equivalent (i.e., a sound introduction to differentiable manifolds). Or, the motivtion to pick up the background material via self-study.

Textbook: Riemannian Geometry, Takashi Sakai, American Mathematical Society 1996. (available at Wheelock Books, potentially cheaper via AMS website).


Other Useful Texts (on reserve at Baker):


(tentative) Deliverables & (tentative) Grading Guide: The following will comprise the written assignments for this term.

Your course grade will probably be computed as follows.

Written HW
Midterm Exam
Final Exam


Students with disabilities: If you have a disability and require disability related accomodations please speak to me and Ward Newmeyer, Director of Student Accessibility Services, as soon as possible so we can find a remedy.


Last Updated 2 January, 2013