Video Lectures (15)
15 lectures, from vectors and metric spaces through the geometry of curves to connections, parallel transport and the Gauss–Bonnet theorem.
Where these lectures come from
The Curves chapter is by Faculty of Khan. The foundations and the curvature-and-connections chapters are from Math Infinitum's series Differential Geometry: From Curves to Manifolds.
Euclidean Geometry: Vectors, Norms, Dot Products & Metric Spaces
Euclidean vs. Non-Euclidean Geometry: Spherical & Hyperbolic
The Geometry of Curves: A Visual Introduction
Introduction to Differential Geometry: Curves
Arc Length and Reparameterization
Arc Length as a Parameter
Closed Curves and Periodic Curves
Curvature: Intuition and Derivation
Torsion and Special Planes
The Frenet-Serret Formulas