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第25講 Gauss-Bonnet Theorem (cont.)
課程影音
L25A
L25A
1. Theorem: Gauss-Bonnet Theorem for Orientable Compact Surface
2. Example: Sphere with Radius r
3. Example: Convex Surface in R^3
4. Example: Polar Cap
L25B
1. Example: Polar Cap (cont.)
2. Euler Characteristic Number and Genus
3. Theorem: Diffeomorphic Surfaces Have the Same Euler Characteristic
Number and Two Compact Oriented Surfaces with the Same Euler
Characteristic Number Are Diffeomorphic
L25C
1. Theorem: A compact Oriented Surface with Positive Gauss Curvature
Is Diffeomorphic to a Standard Sphere
2. Four Color Map Theorem
1. Theorem: Gauss-Bonnet Theorem for Orientable Compact Surface
2. Example: Sphere with Radius r
3. Example: Convex Surface in R^3
4. Example: Polar Cap
L25B
1. Example: Polar Cap (cont.)
2. Euler Characteristic Number and Genus
3. Theorem: Diffeomorphic Surfaces Have the Same Euler Characteristic
Number and Two Compact Oriented Surfaces with the Same Euler
Characteristic Number Are Diffeomorphic
L25C
1. Theorem: A compact Oriented Surface with Positive Gauss Curvature
Is Diffeomorphic to a Standard Sphere
2. Four Color Map Theorem
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