Elementary Differential Geometry
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Curves in the plane and in space.- How much does a curve curve?.- Global properties of curves.- Surfaces in three dimensions.- Examples of surfaces.- The first fundamental form.- Curvature of surfaces.- Gaussian, mean and principal curvatures.- Geodesics.- Gauss' Theorema Egregium.- Hyperbolic geometry.- Minimal surfaces.- The Gauss-Bonnet theorem.
[1] A. Gray. Modern Differential Geometry of Curves and Surfaces , 1993 .
[2] John Oprea. Differential Geometry and Its Applications , 1996 .
[3] V. Rovenski. Geometry of Curves and Surfaces with MAPLE , 2000 .