Math 562 (Spring, 2004)

Introduction to Differential,  Riemann-Finsler Geometry and Topology

Instructor: Z. Shen, Ph.D.

Office: LD 224D

Office Hour: Monday & Wednesday at 12:00-1:00PM or by appointment

Email: zshen@math.iupui.edu;  Phone: 317-278-1065; Voice & Fax: 317-245-0012

Tentative Topics:

1. Differential-Geometric Properties of Curves

2. The Complete System of Invariants for Space Curves

3. Surfaces and Curves on Surfaces

4. Intrinsic Geometry of Surfaces

5. Curvature of Surfaces

6. Special Topics in the Theory of Surfaces

7. The Concept of a Differential Manifold

8. Tensor Algebra

9. Tensor Analysis

10. The Geometry of a Space with Affine Connection

11. Foundation of Riemannian Geometry

12. Finsler Geometry and Characterizations of Riemannian geometry

13. Curves in the Large

14. Surfaces in the Large and the Gauss-Bonnet Theorem

15. Differential Forms, the Exterior Derivative and DeRham Cohomology Groups