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Differential Geometry

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Curves

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Chapter 1.1Basic Concepts
Chapter 1.2Arc Length
Chapter 1.3Tangent Line, Unit Tangent Vector, and Normal Plane
Chapter 1.4Osculating Plane
Chapter 1.5Normal Line and Principal Unit Normal Vector
Chapter 1.6Curvature and Osculating Circle
Chapter 1.7Binormal Vector, Binormal Line, and Rectifying Plane
Chapter 1.8Torsion
Chapter 1.9Frenet-Serret Formulae
Chapter 1.10Vector of Darboux
Chapter 1.11Unit Spherical Indicatrices
Chapter 1.12Approximate Curves
Chapter 1.13Contact and Osculating Sphere

Surfaces

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First Fundamental Form

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Tensors

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Second Fundamental Form

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Geodesics

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Mappings

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Absolute Differentiation, Displacement

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Special Surfaces

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