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課程名稱 |
微分幾何二
Differential Geometry (Ⅱ) |
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開課學期 |
112-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
李瑩英 |
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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 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期三9(16:30~17:20)星期五3,4(10:20~12:10) |
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上課地點 |
天數305天數305 |
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備註 |
研究所數學組基礎課。
總人數上限：40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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Based on the material covered by Differential Geometry I last semester on differentiable manifolds and Riemannian Geometry, we would like to introduce some special topics in this course. It will include
(1) Hodge Theorem
(2) Minimal submanifolds
(3) Heat equation and geometric flows
The topics would be possibly modified according to students' interests and as the class proceeds. If there is time, we would also explore to other topics such as Harmonic Maps and others. Another important part of the course is final project. Every student is required to choose a specific topic/paper and write a final report as well as some presentations.
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課程目標 |
1. Explore to some advanced topics in Differential Geometry and set foundation for research in the area.
2. Equip the students with abilities for independent studies, presentations and conducting research. |
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課程要求 |
This course assumes knowledge covered by the course of Differential Geometry (I). |
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預期每週課後學習時數 |
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Office Hours |
每週二 14:00~15:00 備註： 1.助教Office hour@天數445
*教授Office hour時間另約 |
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指定閱讀 |
For Hodge Theorem, it would be
(a) Frank Warner, Foundations of differentiable manifolds and Lie groups. Chap 6
(b) Chin-Lung Wang, Differential Geometry. Chap 4
For minimal submanifolds
(a) H. B. Lawson, Lectures on Minimal submanilds Vol 1
For 1st and 2nd variational formula of area Chap. 1 . 1, 1.2, 1,9
Examples: 3.1
Weierstrass representation 3.3
Plateau Problem 2.1
(b) Chin-Lung Wang, Differential Geometry. Chap 6 |
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參考書目 |
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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. |
homework |
35% |
including in class participation |
2. |
exams |
30% |
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3. |
project |
35% |
including a written final report and presentations/videos |
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