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課程名稱 |
微分幾何二
Differential Geometry (Ⅱ) |
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開課學期 |
102-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
張樹城 |
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課號 |
MATH7302 |
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課程識別碼 |
221 U2940 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三8(15:30~16:20)星期五3,4(10:20~12:10) |
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上課地點 |
天數102天數102 |
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備註 |
研究所數學組基礎課。
總人數上限：30人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
An introduction to the modern theory of differential geometry, including both the linear and non-linear methods. The linear theory will include the theory of vector bundles as well as the theory of Yang-Mills. The non-linear theory will include an introduction to nonlinear methods in Riemannian and Kaehler manifolds as well as sphere theorem and the Ricci flow. In particular, we will
focus on
1. Curvature in the Vector Bundle and Yang-Mills.
2. An Introduction to Kaehler Manifolds.
3. An introduction to Non-Linear Methods in Riemannian an Kaehler Manifolds.
4. Global Properties in Riemannian Manifolds, such as the Topology Sphere Theorem.
5. Differential Sphere Theorem and the Ricci Flow.
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課程目標 |
Provide an essential foundation in modern geometry, with emphasizes on developments after 1950, and open a way to pursue work or research in differential topology and differential geometry. |
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課程要求 |
Differential Geometry (I) |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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參考書目 |
1. Jurgen, Jost: Riemannian Geometry and Geometric Analysis.
2. J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland, Amsterdam, 1975.
3. R. Schoen and S.T. Yau: Lectures on Differential Geometry.
4. J. Jost, Non-Linear Methods in Riemannian an Kaehler Manifolds.
5. Ben Andrews and Christopher Hopper, The Ricci Flow in Riemannian Geometry, A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem. |
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指定閱讀 |
The related papers for the report. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
home works |
50% |
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2. |
report |
50% |
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