CR REDUCTION ON A CIRCLE BUNDLE OVER A COMPLEX MANIFOLD

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：21

、訪客IP：13.59.250.227

姓名

林京民(Ching-Min Lin) 查詢紙本館藏

畢業系所

數學系

論文名稱

(CR REDUCTION ON A CIRCLE BUNDLE OVER A COMPLEX MANIFOLD)

相關論文

★ Witten Deformation and Morse Inequalities	★ Riemann-Roch-Hirzebruch Theorem For Circle Bundle Over A Riemann Surface
★ 射影變換群之探討	★ Subdivergence theorem on Heisenberg group
★ Asymptotics of the Bergman Kernel for Positive Line Bundles

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 柯西黎曼流形
★ 圓叢
★ 約化與量子化的交換性

關鍵字(英)

★ CR manifold
★ circle bundle
★ Symplectic reduction
★ Guillemin-Sternberg theorem
★ quantization commuting with reduction

論文目次

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

參考文獻

C. Albert, {Le théorème de réduction de Marsden-Weinstein en géométrie cosymplectique et de contact}, J. Geom. Phys., {6} (1989), 627-649.

Cannas da Silva, {Lectures on symplectic geometry}, Lecture Notes in Mathematics, {1764}, Springer-Verlag, Berlin, 2001.

J.-H. Cheng, C.-Y. Hsiao and I.-H. Tsai, {Heat kernel asymptotics and a local index theorem for CR manifolds with S^1 action}, ArXiv:1511.00063.

H. Geiges, {Constructions of contact manifolds}, Math. Proc. Cambridge Philos. Soc., {121} (1997), no. 3, 455-464.

V. Guillemin and S. Sternberg, {Geometric quantization and multiplicities of group representations}, Invent. Math. {67} (1982), no. 3, 515-538.

G. Heckman and P. Hochs, {Geometry of the momentum map}, Lecture notes, (2012).

C.-Y. Hsiao and R.-T. Huang, {G-invariant Szegö kernel asymptotics and CR reduction}, arXiv: 1702.05012.

B. Kostant, {Quantisation and unitary representations}, Lecture notes in Mathematics, Springer-Verlag, 1970.

F. Loose, {A remark on the reduction of Cauchy-Riemann manifolds}, Math. Nachr., {214} (2000), 39-51.

X. Ma, {Hamiltonian manifolds and geometric quantization}. Lecture notes.

J. Marsden and A. Weinstein, {Reduction of symplectic manifolds with symmetry}, Reports on mathematical physics 5, 1974, 121-130.

J. M. Souriau, {Structures des systémes dynamiques}, Dunod, 1970.

指導教授

黃榮宗(Rung-Tzung Huang)

審核日期

2018-7-6

推文