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課程名稱 |
微分幾何二
Differential Geometry (Ⅱ) |
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開課學期 |
111-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
蔡忠潤 |
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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101天數102 |
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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 |
There are three parts:
(1) vector bundles and characteristic class
(2) minimal submanifolds
(3) heat kernel and isometric embedding
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課程目標 |
Provide an essential foundation in differential geometry, and the idea about how to use calculus/analysis to study geometry. |
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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 |
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指定閱讀 |
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參考書目 |
(1) Shigeyuki Morita, Geometry of differential forms [ch. 5]
(2a) notes by Rick Schoen: https://e.math.cornell.edu/people/XinZhou/Math286_2012.pdf
(2b) notes by Chin-Lung Wang: http://www.math.ntu.edu.tw/~dragon/Lecture%20Notes/DG-2020/DG-spring-2021-NTU-Ch6.pdf
(3a) S. Rosenberg, The Laplacian on a Riemannian manifold: An introduction to analysis on manifolds. London Mathematical Society Student Texts, 31. 1997.
(3b) P. Bérard, G. Besson & S. Gallot, Embedding Riemannian manifolds by their heat kernel: https://link.springer.com/article/10.1007/BF01896401
(3c) P. Bérard, Spectral geometry: direct and inverse problems, Springer Lecture Notes in Math. 1207, 1986.
(3d) Xiaowei Wang, Ke Zhu, Isometric embeddings via heat kernel, https://projecteuclid.org/journals/journal-of-differential-geometry/volume-99/issue-3/Isometric-embeddings-via-heat-kernel/10.4310/jdg/1424880984.full |
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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 |
30% |
You have two jokers: the lowest two grades will be discarded. |
2. |
midterm |
35% |
April 14 |
3. |
final |
35% |
June 9 |
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