Differential Geometry (858G1)

15 credits, Level 7 (Masters)

Autumn 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

100%: Lecture

Assessment

20%: Coursework (Portfolio, Problem set)
80%: Examination (Computer-based examination)

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 2021/22. We also plan to offer it in future academic years. However, we are constantly looking to improve and enhance our courses. There may be changes to modules in response to student demand or feedback, changes to staff expertise or updates to our curriculum. We may also need to make changes in response to COVID-19. We’ll make sure to let our applicants know of material changes to modules at the earliest opportunity.