Ma 157b: Riemannian Geometry II

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Instructor: Alexander Gorodnik
Office: 172 Sloan
Phone: 395-4325
E-mail: gorodnik "at" caltech "dot" edu
Office Hours: TBA and by appointment

Course Objective: Math 157b is continuation of Math 157a. Depending on time constrains and student preferences, We will cover some of the following topics:

• Symmetric and locally symmetric spaces
• Comparison methods and results about pinched curvature
• Geodesic flow (closed geodesics and chaotic behavior)
• Structure of manifolds of nonpositive curvature and rigidity
• Spectral theory (eigenvalues of Laplacian, trace formulas)

Prerequisites: Math 157a

Grading Policy: Homework problems will be collected.

References:

• Ballmann, Lectures on Spaces of Nonpositive Curvature, Birkhauser, 1995
• Do Carmo, Riemannian Geometry, Springer-Verlag, 1992
• Eberlein, Geometry of Nonpositively Curved Manifolds, University of Chicago Press, 1997
• Eberlein, Geodesic flows in manifolds of nonpositive curvature, Proc. Symposia in Pure Math., vol. 69 (2001), 525-571
• Gallot, Hulin and Lafontaine, Riemannian Geometry, Springer-Verlag, Universitext, 2004
• Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, AMS, 2001
• Jost, Riemannian Geometry and Geometric Analysis, Springer-Verlag, 2002
• Sakai, Riemannian Geometry, AMS, 1996