課程說明(Course Desc<x>ription)：
<br>本課程是微分幾何 (II)。課程內容包括光滑流形,黎曼幾何,曲率概念完整的描述及其拓撲和分析的基本知識。
<br>為更專業的幾何研究和其它相關領域課程基礎。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
<br>重要問題、理論與其應用。
<br>
<br>
<br>This is an introductory course on differential geometry. It deals with some basic
<br>aspects of geometry, topology and analysis of smooth manifolds. 
<br>
<br>In Differential geometry II,
<br>we introduce the basic tools of Riemannian geometry,
<br>including connections, geodesics and curvature. 
<br>Then we study Completeness and Hopf-Rinow Theorem manifolds with constant 
<br>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 
<br>student interests.
<br>
<br>
<br>References:
<br>Do Carmo: Riemannian Geometry. Chapters 0-4,7-8 
<br>J. Lee: Introduction to smooth manifolds.
<br>S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Universitext, 
<br>Springer.
<br>Warner: Foundations of Differential Manifolds and Lie Groups. 
<br>Jost: Riemannian Geometry and Geometric Analysis.  
<br>
<br>
<br>Homework