MAT 362 - Differential Geometry




Books
For more about curves and surfaces in R3:
  • O'Neill, Elementary Differential Geometry
  • Millman & Parker, Elements of Differential Geometry
The same material is presented from a completely different point of view in Differential Forms with Applications to the Physical Sciences by Harley Flanders.

For a more advanced treatment of Differential Geometry in higher dimensions:
  • doCarmo, Riemannian Geometry
  • Gallot, Hulin, & LaFontaine, Riemannian Geometry
  • Spivak, A Comprehensive Introduction to Differential Geometry
Flatland, the 1880 book about life in a two dimensional universe, is available free online . If you don't like to read books online, Dover publishes an edition for only $1.50.


Gallery of Surfaces


Mathematica programs
  • I have written a Mathematica notebook to allow you to construct your own minimal surfaces by specifying the Weierstrass data. It includes several examples and a brief description of how to determine the conjugate minimal surface and the associated family.



Papers
Many recent publications are available online at the e-Print archive.


Online resources
A lot of good work is being done by the gang at Amherst. Their website includes several galleries of minimal (and other related) surfaces.