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課程名稱 |
微分幾何二
DIFFERENTIAL GEOMETRY (II) |
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開課學期 |
96-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
梁惠禎 |
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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 |
星期二5,6,7(12:20~15:10) |
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上課地點 |
新405 |
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備註 |
先修:高微，研究所數學組基礎課。
總人數上限：50人 |
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課程網頁 |
http://idv.sinica.edu.tw/ftliang/ |
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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 |
(1) differential forms; de Rham cohomology, the Hodge star; harmonic forms;
-----basic spectral geometry:
-----------eigenvalue comparison; isoperimetric inequalities;
-----------heat kernel, Atiyah-Singer index theorems and 4-manifolds; Gauss-Bonnet theorems
(2) geodesic dynamics: Morse theory; Floer Homology
(3) the geometric hierarchy; symmetric spaces; Einstein manifolds; Kahler manifolds;
(4) spinors; Dirac operators; positive mass theorems; variational problems from quantum field theory
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課程目標 |
** |
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課程要求 |
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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 |
Textbooks:
S. Gallot, D. Hulin, J. Lafontaine: Riemannian Geometry, 3rd edition, 2004, Springer
J. Jost, Riemannian Geometry and Geometric Analysis, 4th edition, 2005, Springer
References:
[1] I. Chavel: Riemannian Geometry--a modern introduction, 2006, Cambridge Univ. Press
[2] I. Chavel: Eigenvalues in Riemannian Geometry, 1984, Academic Press
[3] S. Rosenberg: The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds, 1997, London Mathematical Society Student Texts
[4] P. Peterson, Riemannian Geometry, 1998, Springer
[5] A. Besse, Einstein manifolds, 1987, Springer
[6] T M. Berger, A Panoramic View of Riemannian Geometry, 2003, Springer
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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 |
60% |
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2. |
Midterm |
20% |
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3. |
Final |
20% |
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