B3.2 Geometry of Surfaces (2024-25)

Section outline

• Select section General

  General

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  • Select activity Announcements

    

    Announcements Forum
  • Select activity Reading List

    

    Reading List URL
  • Select activity Discussion Forum

    

    Discussion Forum
• Select section Course Materials

  Course Materials

  • Select activity Sheet 0

    

    Sheet 0 Assignment

    This is an initial optional problem sheet to get you started before the classes. Do not hand in solutions.
    
    The questions cover the various background material that is useful to the course - first year geometry, second year complex analysis, topology, projective geometry and multivariable calculus.
    
    Do not be put off by this list of courses as only elements of each course are relevant. Supporting reading appears in the background material in Chapter 0 of the lecture notes.
    
  • Select activity Sheet 1

    

    Sheet 1 Assignment

    This sheet covers the classification theorem for topological surfaces and also has some early examples of smooth, geometric surfaces. Hand in solutions to the Part B exercises. Solutions are provided for the Part A (routine and optional) and Part C (optional extension) exercises.
  • Select activity Sheet 2

    

    Sheet 2 Assignment

    This sheet covers the local geometry of smooth surfaces, the fundamental forms, curvature and the Theorema Egregium. Hand in solutions to the Part B exercises. Solutions are provided for the Part A (optional and mainly calculations) and Part C (optional extension) exercises.
    
  • Select activity Sheet 3

    

    Sheet 3 Assignment

    Exercises on geodesics, the Gauss-Bonnet theorem and applications and the hyperbolic plane. Hand in solutions to Part B. There are also optional more routine questions (Part A) and optional extension questions (Part C ) if helpful.
  • Select activity Sheet 4

    

    Sheet 4 Assignment

    This sheets covers the later of the material on hyperbolic surfaces, and the material on Riemann surfaces including the Riemann-Hurwitz formula.
  • Select activity Synopsis by lecture

    

    Synopsis by lecture File

    I will not lecture the synopsis in the order it is published. Instead the Riemann surface material will be moved to the end of the course and, after the classification theorem, I will move directly on to the local and global real differential geometry.

  • Select activity All lecture notes in a single searchable PDF

    

    All lecture notes in a single searchable PDF File
  • Select activity Useful additional material 1. Nigel Hitchin's lecture notes from 2013

    

    Useful additional material 1. Nigel Hitchin's lecture notes from 2013 File
  • Select activity Useful additional material. 2. Segal's Institute notes. They do not cover the material on Riemann surfaces.

    

    Useful additional material. 2. Segal's Institute notes. They do not cover the material on Riemann surfaces. File
  • Select activity Useful additional material 3. These are Dominic Joyce's handwritten slides for the pre-recorded lectures in the COVID year 2020,

    

    Useful additional material 3. These are Dominic Joyce's handwritten slides for the pre-recorded lectures in the COVID year 2020, File
  • Select activity Useful additional material. 4. Alex Ritter's lecture notes from 2018

    

    Useful additional material. 4. Alex Ritter's lecture notes from 2018 File
• Select section Intercollegiate Classes

  Intercollegiate Classes

  • Select activity Class Signup

    

    Class Signup Class registration

    Registration start: Monday, 7 October 2024, 12:00 PM

    Registration end: Friday, 8 November 2024, 12:00 PM
  • Select activity Class Tutor's Comments

    

    Class Tutor's Comments Assignment

    Class tutors will use this activity to provide overall feedback to students at the end of the course.
    

    Not available unless: You have signed up to a class