L25_A
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
L25_B
1. Example: Polar Cap (cont.)
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
Number and Two Compact Oriented Surfaces with the Same Euler
Characteristic Number Are Diffeomorphic
L25_C
1. Theorem: A compact Oriented Surface with Positive Gauss Curvature Is Diffeomorphic to a Standard Sphere
1. Theorem: A compact Oriented Surface with Positive Gauss Curvature Is Diffeomorphic to a Standard Sphere
2. Four Color Map Theorem
OCW _ Subtitle List (Geometry II).pdf
