Barrett O'Neill

Professor, Department of Mathematics, UCLA          Email: bon@math.ucla.edu

Topics:  curves and surfaces, computers and surfaces, computers and geodesics, Riemanian geometry, black holes.

Elementary Differential Geometry

Revised Second Edition, Academic Press (Elsevier), March 2006

• Preface
• Contents
• Errors in the original 2nd edition

    The following use the basics of Mathematica
    or sometimes Maple 9.

• Some Surfaces in R⁴ and higher dimensions 
• Drawing Surfaces in R³ using Mathematica
• How to Plot Geodesics on Surfaces: 
  •  The Setup
  •  Geodesics on Two Hills
  •  Geodesics on a Hill-Tower Surface
• Graphics-Assisted Geometry of Surfaces        
  • Curvature of  Kummer's Surface      
  • Dissecting  Kuen's Surface

Semi-Riemannian Geometry:

with Applications to Relativity, Academic Press, 1983

• Preface
• Contents
• Errors

The Geometry of Kerr Black Holes

A K Peters, 1995

• Preface
• A Short History of Black Holes
• Overview of a Kerr Black Hole
• Contents
• The Search for Black Holes (has some pictures).

A Few Websites

Thanks to Tom Ferguson and others for their help.