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研究生：	林京民 Ching-Min Lin
論文名稱：	CR REDUCTION ON A CIRCLE BUNDLE OVER A COMPLEX MANIFOLD
指導教授：	黃榮宗 Rung-Tzung Huang
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 數學系 Department of Mathematics
論文出版年：	2018
畢業學年度：	106
語文別：	英文
論文頁數：	43
中文關鍵詞：	柯西黎曼流形、圓叢、約化與量子化的交換性
外文關鍵詞：	circle bundle, Symplectic reduction, Guillemin-Sternberg theorem, quantization commuting with reduction
相關次數：	點閱：8 下載：0
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在這篇論文中，我們首先回顧辛約化，尤其是關於約化與量子化的交換性的Guillemin-Sternberg定理。再來我們回顧柯西黎曼約化的構造。最後我們試著在有柯西黎曼條件的凱勒流形上的圓叢上定出Guillemin-Sternberg定理。

In this thesis we first review the symplectic reduction, in particular, the Guillemin-Sternberg theorem about quantization commuting with reduction. Then we review the construction of the CR reduction. Finally we formulate the Guillemin-Sternberg theorem on a circle bundle over a K\"{a}hler manifold in the CR setting.

Chapter 1. Introduction                                                          page1
Chapter 2. Actions of Lie groups on manifolds                 page3
1. Induced vector fields by group actions                          page3
2. The slice theorem                                                                 page4
3. Lifting Lie group actions in vector bundles                   page6
Chapter 3. Symplectic reduction                                          page9
1. Moment map                                                                        page9
2. Symplectic reduction                                                          page10
Chapter 4. Symplectic reductions and prequantizations page13
1. Prequantum line bundle                                                    page13
2. Kähler prequantizations and reduction                         page15
Chapter 5. CR reduction                                                         page19
1. CR manifolds                                                                        page19
2. Contact reduction                                                              page21
3. CR reduction                                                                        page21
Chapter 6. CR reduction on a circle bundle over a complex manifold                page25
Bibliography                                                                              page29
                                

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