10602 幾何二

  • 幾何二
  • 第25講 Gauss-Bonnet Theorem (cont.)

第25講 Gauss-Bonnet Theorem (cont.)

課程影音

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.)
   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


 
L25_C
   1. Theorem: A compact Oriented Surface with Positive Gauss Curvature Is Diffeomorphic to a Standard Sphere
   2. Four Color Map Theorem