Introduction to Differential Geometry L15480
Nan-Kuo HO
Department of Mathematics
National Cheng-Kung University, Taiwan
September 19, 2003
Schedule
Tuesday 11-12am and Thursday 8-10am. Room: Math building 3177.
Course Outline
This will be a basic introduction to differential geometry. The material that will be covered in the course includes the following:
1. Submanifolds, smooth manifolds
2. Smooth maps between manifolds, immersions, embeddings
3. Tangent and cotangent spaces, tangent and cotangent bundles, vector bundles 4. Differential formes, exterior derivative,
5. Vector fileds, flows on manifolds, Lie derivative, 6. Integration on manifolds, Stokes’ theory
If times permits, an introduction of Poincare lemma, and de Rham cohomology will be given.
Grading
There will be no midterm or final. Assignments and 5-10 mins final presentation topics will be given during the semester.
Office hours
Walk-in or by appointment.
Suggested reading
1. V.Guillemin and A.Pollack, Differential Topology, 1974 2. L.Conlon, Differentiable manifolds: A First Course, 1993
1
3. M.Spivak, Calculus on Manifolds, 1965
4. I.M.Singer and J.A.Thorpe, Lecture notes on Elementary Topology and Geometry, UTM.
5. W.Boothby, An Introduction to Differential Manifolds and Riemannian Geometry, 1986
6. R.Bott and L.Tu, Differential Forms in Algebraic Topology, 1982
7. M.Spivak, A Comprehensive Introduction to Differential Geometry, (Vol 1), 1979.
2
