Introduction to Differential Geometry
                                    L15480
                                  Nan-Kuo HO
                               Department of Mathematics
                          National Cheng-Kung University, Taiwan
                                                     January 28, 2004
                Schedule
                   Tuesday 10:30-12am and Thursday 11:30am-1pm. Room: Math build-
                   ing 3177.
                Course Outline
                   This term we will focus on Riemannian geometry. The material that
                   will be covered in the course includes the following:
                     1. Differentiable manifolds
                     2. Riemannian metric
                     3. Parallel transport and Connections
                     4. Geodesics : geodesic flow, minimizing properties
                     5. Curvature : Sectional, Ricci, scalar curvature
                     6. Jacobi field
                     7. The second fundamental form
                     8. Variations of energy
                   If times permits, an introduction of Morse theory will be given.
                Grading
                   There will be one final exam. Assignments will be given during the
                   semester.
                Office hours
                   Walk-in or by appointment.
                Suggested reading
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               1. Jurgen Jost, Riemannian Geometry and Geometric Analysis
               2. do Carmo, Riemannian Geometry
               3. L.Conlon, Differentiable manifolds: second edition, 2001
               4. Jeff Cheeger and David Ebin, Comparison Theorems in Rieman-
                nian Geometry
               5. W.Boothby, An Introduction to Differential Manifolds and Rie-
                mannian Geometry, 1986
               6. Frank Warner, Foundations of Differentiable Manifolds and Lie
                Groups
               7. M.Spivak, A Comprehensive Introduction to Differential Geome-
                try, (Vol 1), 1979.
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