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Differential Geometry
Folder: Study/Differential-Geometry
25 items under this folder.
Aug 31, 2025
1-2. Parametrized Curves
Aug 31, 2025
1-3. Regular Curves; Arc Length
Aug 31, 2025
1-4. The Vector Product in R³
Aug 31, 2025
1-5. The Local Theory of Curves Parametrized by Arc Length
Aug 31, 2025
1-6. The Local Canonical Form
Aug 31, 2025
1-7. Global Properties of Plane Curves
Aug 31, 2025
2-2. Regular Surfaces; Inverse Images of Regular Value
Aug 31, 2025
2-3. Change of Parameters; Differentiable Functions on Surface
Aug 31, 2025
2-4. The Tangent Plane;The Differential of a Map
Aug 31, 2025
2-5. The First Fundamental Form; Area
Aug 31, 2025
2-6. Orientation of Surfaces
Aug 31, 2025
2-7. A Characterization of Compact Orientable Surfaces
Aug 31, 2025
2-8. A Geometric Definition of Area
Aug 31, 2025
2-Appendix. A Brief Review of Continuity and Differentiability
Aug 31, 2025
3-2. The Definition of the Gauss Map and Its Fundamental Properties
Aug 31, 2025
3-3. The Gauss Map in Local Coordinates
Aug 31, 2025
3-4. Vector Fields
Aug 31, 2025
3-5. Ruled Surfaces and Minimal Surfaces
Aug 31, 2025
3-Appendix. Self-Adjoint Linear Maps and Quadratic Forms
Aug 31, 2025
4-2. Isometries; Conformal Maps
Aug 31, 2025
4-3. The Gauss Theorem and the Equations of Compatibility
Aug 31, 2025
4-4. Parallel Transport. Geodesics.
Aug 31, 2025
4-5. The Gauss-Bonnet Theorem and Its Applications
Aug 31, 2025
4-6. The Exponential Map. Geodesic Polar Coordinates
Aug 31, 2025
Differential Geometry