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.

Teaching and assessment

We’re currently reviewing teaching and assessment of our modules in light of the COVID-19 situation. We’ll publish the latest information as soon as possible.

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

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.


This module is offered on the following courses: