Differential Geometry Book List

As I continue preparing for a differential geometry course that might not run, I am assembling a bibliography for my students. (It is far too sad to contemplate that the course won’t run. I will just Keep Calm and Continue Planning.)
I want to hand them an annotated bibliography, with some reasonable commentary about the quality, content and outlook of the texts on the list.

Elementary Differential Geometry Books

This job is turning out to be a rather large one. There are lots of elementary differential geometry texts. Not quite as many as calculus or linear algebra, but still.

So I will break the job into some more manageable pieces. I’ll start with a simple book list. These are the fruits of an afternoon’s search for possible introductory texts. Later, I will fill in with miniature reviews of the books as I take a more detailed look at them. I have every intention of starting this project strong and then watching it slowly fade into a guilty state of incompletion. But who knows? Maybe this is actually something I can finish.

The Great Elementary Differential Geometry Textbook Review of Winter 2012

A note on the definition of “elementary”: I will only consider texts that I think have some outside chance of serving as a stand-alone introduction to the classical differential geometry of curves and surfaces in \mathbb{R}^3. The prerequisites should be no more than courses in multivariable calculus and linear algebra. A few books presuppose a passing familiarity with differential equations. I will allow this, but if the text assumes material past what might reasonably be covered in the course of the regular calculus sequence it will be removed from the list.

I have cut out many books simply because they are too advanced. When I am done with the list of elementary books, I will likely include a short list of my favorite “advanced books” and some other reference material I think is interesting.

I found over 20 books without much effort, so this might take a bit of work.

The List

In no particular order, the books I will look at are:

  • Stoker, Differential Geometry
  • Wardle, Differential Geometry
  • Kreyszig, Differential Geometry
  • Willmore, An Introduction to Differential Geometry
  • Struik, Lectures on Classical Differential Geometry
  • O’Neill, Elementary Differential Geometry
  • Oprea, Differential Geometry and its Applications
  • Snygg, A New Approach to Differential Geometry Using Clifford’s Geometric Algebra
  • Pressley, Elementary Differential Geometry
  • Toponogov, Differential Geometry of Curves and Surfaces
  • Thorpe, Elementary Topics in Differential Geometry
  • McCleary, Geometry from a Differential Viewpoint
  • Kühnel, Differential Geometry: Curves – Surfaces – Manifolds, 2nd Ed.
  • Bär, Elementary Differential Geometry
  • Montiel & Ros, Curves and Surfaces, 2nd Ed.
  • Millman & Parker, Elements of Differential Geometry
  • do Carmo, Differential Geometry of Curves and Surfaces
  • Banchoff and S. Lovett, Differential Geometry of Curves and Surfaces
  • Gray, Modern Differential Geometry of curves and Surfaces with Mathematica
  • Vaizman, A First Course in Differential Geometry
  • Spivak, A Comprehensive Introduction to Differential Geometry, vols 1-5
  • Shifrin, Differential Geometry: A First Course in Curves and Surfaces
  • Henderson, Differential Geometry: A Geometric Introduction
  • Weatherburn, Differential Geometry of Three Dimensions

There are a couple of other texts, I suppose. I found these by going through major publishers websites and looking through UNI’s Rod Library stacks. A few of these have been on my shelf for a while, but I haven’t really taken time to read some significant portion and decide if I like them.

Have I mentioned that I have a problem? Yeah, I spend too much money on mathematics books.