Chapter 6 • The First and Second Fundamental Forms




6.1: The First Fundamental Form


Example 6.1.3: The xy-Plane


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Example 6.1.4: Cylinder


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Example 6.1.5: Spheres


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Page 148: Arc Length for General Curves on Surfaces


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Example 6.1.6: Loxodromes


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Proposition 6.1.7: Area


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Example 6.1.8


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6.2: The Gauss Map


Definition 6.2.1: Gauss Map and Example 6.2.2: Gauss Map on a Sphere


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Example 6.2.3: Elliptic Paraboloid


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Example 6.2.4: Hyperbolic Paraboloid


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Page 165: Differential of the Gauss Map






6.3: The Second Fundamental Form


Definition 6.3.2: Second Fundamental Form


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Example 6.3.3: Spheres


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Page 169: Definition of Osculating Paraboloid


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Example 6.3.5: Torus


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Example 6.3.6: Monkey Saddle


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6.4: Normal and Principal Curvatures



Definition 6.4.1: Normal Curvature



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Definition 6.4.5: Principal Curvatures and Principal Directions






6.5: Gaussian and Mean Curvature


Definition 6.5.1: Gaussian Curvature



Definition 6.5.1: Mean Curvature



Example 6.5.4: Function Graphs



Problem 6.5.9: Normal Variations (i.e., Parallel Surfaces)






6.6: Ruled Surfaces and Minimal Surfaces


Problem 6.6.9: Enneper's Surface



Problem 6.6.11: Deformations of Minimal Surfaces





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