Lectures on Differential Geometry

 

Ben Andrews

Australian National University

 

Table of Contents:

 

 
 
 
Lecture 1:  Manifolds 1
Lecture 2:  Smooth Maps 9
Lecture 3:  Submanifolds 17
Lecture 4:  Tangent Vectors 23
Lecture 5:  Lie Groups 35
Lecture 6:  Differential Equations 49
Lecture 7:  Lie Brackets and Integrability 59
Lecture 8:  Connections 71
Lecture 9:  Riemannian Metrics 87
Lecture 10:  The Levi-Civita Connection 95
Lecture 11:  Geodesics and Completeness 101
Lecture 12:  Tensors 109
Lecture 13:  Differential Forms 119
Lecture 14:  Stokes' Theorem 129
Lecture 15:  de Rham Cohomology  137
Lecture 16:  Curvature 151
Lecture 17:  Extrinsic Curvature 165
Lecture 18:  The Gauss and Codazzi Equations 171
Lecture 19:  Cartan's Moving Frame Method 177
Lecture 20:  The Gauss-Bonnet Theorem 181