透過使用調和映射的Bochner技巧, Siu[15, 16]證明了對於複維數≥2 時不可約對稱域緊致商空間的複結構的強剛定理. 其後在[9]中, Mok 證明了在任何秩≥2 的不可約對稱域緊致商空間上, 所有具備非正全純雙截曲率的Hermitian 度量必然和典範度量相差一個常數因子. 由這個定理和Siu 的定理可以得出Mostow 剛性定理[14]在特殊情形下的推廣.本論文會對Mok的結果作出研究. / By using Bochner technique of harmonic maps, Siu[15, 16] proved a strong rigidity theorem concerning the complex structure of compact quotients of irreducible bounded symmetric domain of complex dimension≥ 2. Later in [9], Mok proved a metric rigidity theorem which asserts that any Hermitian metric of seminegative holomorphic bisectional curvature on a compact quotient of an irreducible bounded symmetric domain of rank≥ 2 is necessarily a constant multiple of the canonical metric. This theorem together with the theorem of Siu yields a generalization of a special case of Mostow's rigidity theorem[14]. This thesis is an exposition of Mok's results. / Detailed summary in vernacular field only. / Li, Ka Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 102-104). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Symmetric Space --- p.5 / Chapter 2.1 --- Riemannian Symmetric Spaces --- p.5 / Chapter 2.2 --- Lie Groups and Lie Algebras --- p.10 / Chapter 2.3 --- Riemannian Symmetric Spaces of Compact and Non-compact type --- p.11 / Chapter 2.4 --- Hermitian Symmetric Spaces --- p.16 / Chapter 2.5 --- Duality --- p.19 / Chapter 3 --- Some Embedding Theorems --- p.22 / Chapter 3.1 --- The Borel Embedding Theorem --- p.22 / Chapter 3.2 --- Root Space Decomposition and Root System --- p.24 / Chapter 3.3 --- The Polydisc Theorem --- p.28 / Chapter 3.4 --- The Harish-Chandra Embedding Theorem --- p.36 / Chapter 4 --- Bounded Symmetric Domains --- p.42 / Chapter 4.1 --- Classical Bounded Symmetric Domains --- p.42 / Chapter 4.2 --- The Bergman metric --- p.57 / Chapter 5 --- Projective and Characteristic Bundle --- p.65 / Chapter 5.1 --- Projectivization of Hermitian Vector Bundle --- p.65 / Chapter 5.2 --- Characteristic bundle --- p.69 / Chapter 6 --- The Hermitian Metric Rigidity Theorem --- p.83 / Chapter 7 --- Appendix --- p.100 / Bibliography --- p.102

Thesis (Ph.D.)--York University, 2006. Graduate Programme in Mathematics. / Typescript. Includes bibliographical references (leaves 95-97). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR19776

No description available.

The thesis mainly studies two problems in Algebraic Geometry and Hodge Theory. The first problem deals with the geometric realizations of certain Hermitian symmetric domains as moduli space of algebraic varieties, notably the Abelian varieties and Calabi-Yau varieties. The study of the first problem occupies most of the thesis. In section 1.3; we study the second problem, namely, the L2 Higgs cohomology of polarized variation of Hodge structures over Hermitian symmetric domains. / Sheng Mao. / "December 2005." / Advisers: Shing-Tung Yau; Nai-Chung Conan Leung. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6442. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 108-113). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

In this thesis, we introduce a new space of Hermitian Jacobi forms, and we determine its structure. As an application, we study heat cycles of Hermitian Jacobi forms, and we establish a criterion for the existence of U(p) congruences of Hermitian Jacobi forms. We demonstrate that criterion with some explicit examples. Finally, in the appendix we give tables of Fourier series coefficients of several Hermitian Jacobi forms.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 112-116).

published_or_final_version / Mathematics / Master / Master of Philosophy

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(理学) / 甲第23693号 / 理博第4783号 / 新制||理||1685(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐藤 昌利, 教授 柳瀬 陽一, 教授 川上 則雄 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy