Differential Geometry (858G1)

15 credits, Level 7 (Masters)

Spring teaching

On this module, we will cover:

  • Manifolds and differentiable structures
  • Lie derivatives
  • Parallel transport
  • Riemannian metrics and affine connections
  • Curvature tensor
  • Sectional curvature
  • Scalar curvature
  • Ricci curvature
  • Bianchi identities
  • Schur's lemma
  • Complete manifolds
  • Hopf-Rinow theorem
  • Hadmard's theorem
  • Geodescis and Jacobi fields
  • Bonnet-Meyer and Synge theorems
  • Laplace-Beltrami operator
  • Heat kernels and index theorem.


100%: Lecture


20%: Coursework (Problem Set)
80%: Examination (Unseen examination)

Contact hours and workload

This module is 150 hours of work. This breaks down into 33 hours of contact time and 117 hours of independent study.

This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.