← Series

Geometry

In this series, we cover some of my favorite topics in geometry. We take quite a wide approach - both through classical Riemannian geometry as well as Cartan's formulation of differential forms and the Generalised Stokes Theorem. This will let us move on nicely to General Relativity that describes the geometry of our spacetime.

3 of 14 published

Start from the beginning

Contents

Part 1 — The Geometry of Space

  1. 1Manifolds and Charts
  2. 2Tangent Vectors and Spaces
  3. 3Covectors and One-Forms
  4. 4Tensors
  5. 5The metric
  6. 6Differential forms and the wedge product
  7. 7The Jacobian
  8. 8The exterior derivative
  9. 9Generalised Stokes Theorem
  10. 10The Lie derivative
  11. 11Killing vectors and isometries
  12. 12Connections and parallel transport
  13. 13Curvature
  14. 14Geodesics and geodesic deviation