C3.11 Riemannian Geometry (2022-23)

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  Course Materials
  • Select activity Sheet 1

    

    Sheet 1 Assignment

    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.
  • Select activity Sheet 2

    

    Sheet 2 Assignment

    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.
  • Select activity Sheet 3

    

    Sheet 3 Assignment

    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.
  • Select activity Sheet 4

    

    Sheet 4 Assignment

    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.
  • Select activity Riemannian Geometry Lecture Notes

    

    Riemannian Geometry Lecture Notes File

    These lectures notes provide all of the essential material for the course, as well as some additional points for interest.
    

  • Select activity Riemannian Geometry Mock Exam

    

    Riemannian Geometry Mock Exam File
  • Select activity Riemann Geometry: Essential formulae

    

    Riemann Geometry: Essential formulae File

    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.