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第11講 The Intrinsic Geometry of Surfaces: Isometries and Conformal
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L11A
L11A
1. Parametrizations for Catenoid and Helicoid
2. Isometry and Local Isometry
3. Example: Local Isometric; The Cylinder and Plane in R^2
L11B
1. Example: Local Isometric; The Cylinder and Plane in R^2 (cont.)
2. Example: Every Helicoid Is Locally Isometric to Catenoid
3. Proposition: Two Regular Surfaces Have the Same First Fundamental
Form in Domain U if and only if They Are Locally Isometric
L11C
1. Proposition: Two Regular Surfaces Have the Same
First Fundamental Form in Domain U if and only if They
Are Locally Isometric (cont.)
2. Conformal
1. Parametrizations for Catenoid and Helicoid
2. Isometry and Local Isometry
3. Example: Local Isometric; The Cylinder and Plane in R^2
L11B
1. Example: Local Isometric; The Cylinder and Plane in R^2 (cont.)
2. Example: Every Helicoid Is Locally Isometric to Catenoid
3. Proposition: Two Regular Surfaces Have the Same First Fundamental
Form in Domain U if and only if They Are Locally Isometric
L11C
1. Proposition: Two Regular Surfaces Have the Same
First Fundamental Form in Domain U if and only if They
Are Locally Isometric (cont.)
2. Conformal
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