Differential Geometry

Lecture Notes


University of Hull


5 Jan 2024


These are the Lecture Notes of Differential Geometry 661955 for T1 2023/24 at the University of Hull. We will study curves and surfaces in \(\mathbb{R}^3\). I will follow these lecture notes during the course. If you have any question or find any typo, please email me at


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


and on the Course Webpage hosted on my website


Digital Notes

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Main textbooks:

Other interesting readings are the books by do Carmo (do Carmo 2017) and Abate, Tovena (Abate, Marco and Tovena, Francesca 2011). 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).


It is important to visualize the geometrical objects and concepts we are going to talk about in this course. I will show basic Python code to plot curves and surfaces. This part of the course is not required for the final examination. 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 course using the excellent online 3D grapher tool CalcPlot3D. To understand how it works, please refer to the help manual or to the short video introduction. Another nice tool is Desmos.


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 final exam.