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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