Transcription of Classical Differential Geometry - UCLA Mathematics
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Classical Differential GeometryPeterPetersenPrefaceThis is an evolving set of lecture notes on the Classical theory of curves andsurfaces. Pictures will be added eventually. I recommend people download3DX-plorMathto check out the constructions of curves and surfaces with this app. Itcan also be used to create new curves and surfaces in parametric form. Other usefuland free apps are Geogebra, Grapher (on Mac), and a minimum a one quarter course should cover sections , , , , , and chapters 4, 5. In a semester course it d be possible to cover more fromchapter 2 and also delve into chapter 6. Chapters 6 and 7 can be covered in asecond quarter class. Note that section is a necessary prerequisite for provingthe general Gauss-Bonnet in section excellent reference for the Classical treatment of Differential Geometry is thebook by Struik [2].
Principal Curvatures 138 Exercises 141 5.5. Ruled Surfaces 144 Exercises 151 Chapter 6. Surface Theory 156 6.1. Generalized and Abstract Surfaces 156 Exercises 161 6.2. Curvature on Abstract Surfaces 162 Exercises 166 6.3. The Gauss and Codazzi Equations 168 Exercises 177 6.4. The Gauss-Bonnet Theorem 181 Exercises 185
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