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03-5715131#35401 mengfen@mx.nthu.edu.tw 吳小姐

Title

Video

Syllabus

## 章節大綱

L25A
線性分式變換 (莫比烏斯變換)、交比

0:00 Linear Fractional Transformations (Möbius Transformations)
線性分式變換 (莫比烏斯變換)

1:55 Fixed Points of a Linear Fractional Transformation 線性分式變換的不動點
12:44 Cross Ratio 交比

L25B
交比
0:00 Cross ratio of any four distinct points is invariant under any linear fractional
transformation.
相異四點的交比在任意線性分式變換之下不變
2:47 Proof 證明
11:10 Find the linear fractional transformation T such that T(a)=α, T(b)=β, T(c)=γ.
找出滿足T(a)=α, T(b)=β, T(c)=γ的線性分式變換T
18:09 Example 例題

L25C

0:00 f is an automorphism of the Riemann sphere if and only
if f is a linear fractional transformation. f是黎曼球上的自同構若且唯若f是線性分式變換
2:15 Manifolds and Local Coordinates 流形和局部坐標
9:17 Local Coordinate Near the Point at Infinity 無窮遠點附近的局部坐標
13:57 Proof of Theorem - Part 1 定理證明第1部分

L25D

0:00 Proof of Theorem - Part 1 (cont.) 定理證明第1部分 (續)
7:52 Proof of Theorem - Part 2 定理證明第2部分
16:35 The cross

### 課程資訊

• #### 程守慶 教授

• 上架日期: 2023-07-19
• 點閱次數: 4578