Math 562           Spring 2002

Zhongmin Shen

zshen@math.iupui.edu 

Introduction to Differential Geometry  and Topology

Tentative Topics:

• Manifolds

• Vector Fields and Differential Forms

• Tangent Bundles and Vector Bundles

• Sprays and Second Order Ordinary Differential Equations

• Examples of Sprays

• Riemann Curvature and Non-Riemannian Curvatures

• Projective Geometry of Sprays

• Distance Functions and Metrics

• Examples of Metrics

• Geodesics

• Riemann Curvature and Non-Riemannian Curvatures

• Projective Geometry of Metrics

• Metrics of Constant Curvature

• Quantum Geometry (if time permits)

Homework