Differential Geometry

Lecture Notes

Author
Affiliation

University of Hull

Published

1 Nov 2024

Welcome

These are the Lecture Notes of Differential Geometry 661955 for 2024/25 at the University of Hull. I will use this material during lectures. If you have any question or find any typo, please email me at

S.Fanzon@hull.ac.uk

Up to date information about the course, Tutorials and Homework will be published on the University of Hull Canvas Website

canvas.hull.ac.uk/courses/73612

Digital Notes

Features of these digital notes:

  • Navigation bar is available on the left
  • A search function is available on the top-right
  • You can toggle dark mode on the top-right
  • A pdf version of these notes is available to download on the top-right

Readings

We will study curves and surfaces in \(\mathbb{R}^3\), as well as some general topology. The main textbooks are:

Other good readings are the books:

I will assume some knowledge from Analysis and Linear Algebra. A good place to revise these topics are the books by Zorich (Zorich 2015, 2016).

Visualization

It is important to visualize the geometrical objects and concepts we are going to talk about in this module. Chapter 5 contains a basic Python tutorial to plot curves and surfaces. This part of the notes is not examinable.

If you want to have fun plotting with Pyhton, I recommend installation through Anaconda or Miniconda. The actual coding can then be done through Jupyter Notebook. Good references for scientific Python programming are (Johansson 2019; Kong, Qingkai, Siauw, Timmy, and Bayen, Alexandre 2020).

If you do not want to mess around with Python, you can still visualize pretty much everything we will do in this module using

Important

You are not expected to purchase any of the above books. These lecture notes will cover 100% of the topics you are expected to known in order to excel in the Homework and Final Exam.