MAU34301 Differential geometry

Assessment Details

• This module is examined in a 2-hour examination at the end of Semester 1.
• Students are assessed based on the exam alone.
• Any failed components are reassessed, if necessary, by an exam in the reassessment session.
• The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows: 
  1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session; 
  2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam; 
  3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

  Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php  Select the year and scroll to the School of Physics.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

Module Content

• Riemmanian metrics
• Plane and Space curves
• Gauss Map and curvature
• Connections and Theorema Egregious, Levi-Civita connection
• Curvature tensor
• Gauss Bonnet
• Geodesics
• Further topics such as: Exponential map, Hopf Rinow

Recommended Reading

• Modern geometry, methods and applications, parts I and II, by Dubrovin, Fomenko and Novikov.
• Geometrical methods of mathematical physics by B. Schutz.
• Differential geometry of manifolds by S. Lovett.
• Lecture notes on general relativity by S.M. Carroll (available here).
• Advanced general relativity by S. Winitzki (available here).