C3.11 Riemannian Geometry (202223)
Section outline


This problem sheet is based on the material in Sections 1 and 2 of the lecture notes.
There are three sections to the problem sheet. Sections A and B consist of core material and Section C consists of a slightly more advanced question.
Students should only hand in solutions to questions in Section B.
There are two files: rg2223_sheet1.pdf contains just the questions and rg2223_sol1.pdf contains the questions and the solutions to the questions in Sections A and C. I would strongly suggest that you attempt Sections A and C without looking at the solutions, as it will be very helpful to you. 
This problem sheet is based on the material in Sections 2.3 and 3 of the lecture notes.
There are three sections to the problem sheet. Section A consists of core material, Section B consists of core material and some more supplementary questions and Section C consists of a more advanced question based on core material.
Students should only hand in solutions to questions in Section B.
There are two files: rg2223_sheet2.pdf contains just the questions and rg2223_sol2.pdf contains the questions and the solutions to the questions in Sections A and C. I would strongly suggest that you try Section A without looking at the solutions. It would also be good to try Section C without getting hints from the solutions. 
This problem sheet is based on the material in Sections 4, 5 and 6 of the lecture notes.
There are three sections to the problem sheet. Section A consists of core material, Section B consists of core material and some more supplementary questions and Section C consists of a significantly more advanced question but which is very interesting and relevant.
Students should only hand in solutions to questions in Section B.
There are two files: rg2122_sheet3.pdf contains just the questions and rg2122_sol3.pdf contains the questions and the solutions to the questions in Sections A and C. I would strongly recommend trying Section A without looking at the solutions first. Section C is more challenging but worth a go, especially as there is a big hint in the question. 
This problem sheet is based on the material in Sections 7, 8 and 9 of the lecture notes.
There are three sections to the problem sheet. Section A consists of core material, Section B consists of core material at a slightly more advanced level and Section C consists of a slightly more advanced style of question.
Students should only hand in solutions to questions in Section B.
There are two files: rg2223_sheet4.pdf contains just the questions and rg2223_sol4.pdf contains the questions and the solutions to the questions in Sections A and C. As always, I strongly recommend trying Section A seriously before looking at the solutions, and you should have a go at Section C before consulting the solutions. 
These lectures notes provide all of the essential material for the course, as well as some additional points for interest.

I give a list of what I consider to be essential formulae for the course. I also give a few useful but not essential formulae.
