Math 562 (Spring, 2008)

Introduction to Differential Geometry and Topology

Instructor: Zhongmin Shen, Ph.D.

Office: LD 224D

Classroom: LD 229

Date & Time: Tuesday & Thursday 3:00pm-4:15pm

Office Hour: Tuesday & Thursday 4:30pm-5:30pm or by appointment

Email: zshen@math.iupui.edu;  Phone: 317-278-1065

Textbook: Lecture notes

Tentative Topics:

  1. Geometric Properties of Smooth 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. Tensors

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

  10. The Geometry of a Space with Affine Connection

  11. Foundation of Riemannian Geometry and Finsler Geometry

  12. Gauss-Bonnet and Poincare theorems on vector fields

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