課程說明(Course Description)：
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<br>本課程為幾何分析基礎入門課程,課程內容為簡介基本的理論與應用。
<br>期望幫助同學在幾何相關領域的學習,帶領學生研讀幾何分析的重要問題、理論與其應用。
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<br>Riemannian geometry provide an important tools in modern mathematics, impacting on diverse areas from 
<br>the pure to applied. 
<br>We introduce the basic tools of Riemannian geometry,
<br>including connections, geodesics and curvature. 
<br>Then we study Completeness and Hopf-Rinow Tehorem manifolds with constant curvature,
<br>The theorems of Bonnet-Myers and of Synge-Weinstein, 
<br>The Rauch comparison theorem and the Sphere Theorem. 
<br>More topics will be covered at the instructor's discretion and depending on student interests.
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<br>References:
<br>Do Carmo: Riemannian Geometry. Chapters 0-4,7-8 
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<br>S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Universitext, Springer.
<br>Warner: Foundations of Differential Manifolds and Lie Groups. 
<br>Jost: Riemannian Geometry and Geometric Analysis.  
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<br>Course score =Homework 50% + examinations 50% 
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