Seminar on Differential Geometry
Student No.:50
Time:Tue./Thu. 10:10-12:00, (Except for public holidays from Sep. 30 to Oct. 7)
Instructor:Dominic Leung  [Purdue University (Emeritus)]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2012-9-4
Ending Date:2012-10-18

Course description:

The first part of the seminar (10 weeks) is an introduction to the basic concepts of differential geometry including, differentiable manifolds and calculus on them, fiber bundles, connections ( including an introduction to connections on principal bundles), Riemannian Geometry, Lie Groups, moving Frames and complex manifolds. The second part (2 weeks) is an introduction to symmetric spaces and the geometry of reflective submanifolds, a currently active area of research. The seminar is tailored for advanced undergraduate and beginning graduate students.




Linear algebra, basic point set topology and analysis on Rn




Reference for the course:

1. S.S. Chern, W.H. Chen and K.S. Lam, Lectures on differential Geometry, (World Scientific, 2000)

2. J.A. Wolf , Spaces of Constant Curvature (6th Edition, AMS Chelsea, 2010)

3. Jurgen Jost, Riemannian Geometry and Geometric Analysis (5th Edition, Springer, 2008)

4.S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Academic Press 1978)

5. Old and recent Journal articles on reflective submanifolds.