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

In this thesis we introduce and study the (i) Grassmannian, (ii) Lagrangian Grassmannian, and (iii) double Lagrangian Grassmannian of subspaces in ( A ⊗ B )n, where A and B are normed division algebras, i.e. R,C,H or O . / This gives a simple and uniform description of all symmetric spaces. This is analogous to Tits magic square description for simple Lie algebras. / We show that every irreducible compact Riemannian symmetric space X must be one of these Grassmannian spaces (up to a finite cover) or a compact simple Lie group. Furthermore, its noncompact dual symmetric space is the open sub-manifold of X consisting of spacelike linear subspaces, at least in the classical cases. / Huang, Yongdong. / "July 2007." / Adviser: Naichung Conan Leung. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0353. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 64-65). / 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.

Chen, Yunxia. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 54-56). / Abstracts in English and Chinese. / Chapter 1 --- Embedding in Hermitian case --- p.8 / Chapter 1.1 --- Basics on Riemannian symmetric spaces --- p.8 / Chapter 1.2 --- Embedding in Hermitian case --- p.11 / Chapter 1.2.1 --- Borel embedding theorem --- p.11 / Chapter 1.2.2 --- Harish-Chandra embedding theorem --- p.12 / Chapter 1.2.3 --- Hermann convexity theorem --- p.14 / Chapter 2 --- Embedding in generalized Grassmannian case --- p.15 / Chapter 2.1 --- Compact symmetric spaces as Grassmannians --- p.15 / Chapter 2.1.1 --- Preliminaries --- p.15 / Chapter 2.1.2 --- "Grassmannians, Lagrangian Grassmannians and Double Lagrangian Grassmannians" --- p.16 / Chapter 2.1.3 --- Compact simple Lie groups --- p.20 / Chapter 2.2 --- Embedding in generalized Grassmannian case --- p.23 / Chapter 2.2.1 --- Space-like Grassmannian --- p.23 / Chapter 2.2.2 --- Graph-like Grassmannian --- p.26 / Chapter 2.2.3 --- Convexity property --- p.27 / Chapter 3 --- Cut locus of Compact symmetric spaces --- p.29 / Chapter 3.1 --- Cut locus --- p.29 / Chapter 3.1.1 --- Cut locus of Riemannian manifold --- p.29 / Chapter 3.1.2 --- Lie algebra of compact symmetric space --- p.31 / Chapter 3.1.3 --- Tangent cut locus of compact symmetric spaces --- p.32 / Chapter 3.2 --- Hermitian case and generalized Grassmannian case --- p.36 / Chapter 3.2.1 --- The Hermitian case --- p.36 / Chapter 3.2.2 --- The generalized Grassmannian case --- p.38 / Chapter 4 --- Construction of the explicit embedding --- p.42 / Chapter 4.1 --- Regular symmetric spaces --- p.42 / Chapter 4.2 --- Embedding in Regular case --- p.45 / Chapter 4.2.1 --- Construction of the embedding --- p.45 / Chapter 4.2.2 --- The properties of the explicit embedding --- p.47 / Chapter 4.3 --- Generalization of the embedding --- p.51 / Bibliography --- p.54

So, Tse Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 55-56). / Abstracts in English and Chinese. / Chapter 1 --- Geometric Quantization --- p.8 / Chapter 1.1 --- Motivation --- p.8 / Chapter 1.2 --- Prequantization --- p.10 / Chapter 1.3 --- Kahler Polarization --- p.14 / Chapter 1.4 --- Holomorphic Quantization and Fock Space --- p.17 / Chapter 1.4.1 --- Example: Fock Space --- p.19 / Chapter 2 --- Projectively Flat Connection --- p.21 / Chapter 2.1 --- Variation of Complex Structure --- p.21 / Chapter 2.2 --- Projectively Flat Connection on H --- p.24 / Chapter 2.2.1 --- Example of n= 1: --- p.30 / Chapter 3 --- Construction of Projectively Flat Connection --- p.34 / Chapter 3.1 --- Mechanism for Construction of Projectively Flat Con- nection --- p.34 / Chapter 3.2 --- K = C Case --- p.39 / Chapter 3.2.1 --- Identification of C´ؤlinear Complex Structures --- p.40 / Chapter 3.2.2 --- Projecitvely flat bundle on U(n)×U(n) --- p.43 / Chapter 3.2.3 --- Example of n=1 --- p.44 / Chapter 3.3 --- K = H Case --- p.45 / Chapter 3.3.1 --- Identification of H-linear Complex Structures --- p.46 / Chapter 3.3.2 --- Projecitvely flat bundle on SO*(4n) --- p.49 / Chapter 3.3.3 --- Example of n = 1 --- p.51 / Bibliography --- p.55

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Thesis (Ph. D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 50-53).

Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let g denote the complexification of the Lie algebra of U, g=u^C. Each u-compatible triangular decomposition g= n_- + h + n_+ determines a Poisson Lie group structure pi_U on U. The Evens-Lu construction produces a (U, pi_U)-homogeneous Poisson structure on X. By choosing the basepoint in X appropriately, X is presented as U/K where K is the fixed point set of an involution which stabilizes the triangular decomposition of g. With this presentation, a connection is established between the symplectic foliation of the Evens-Lu Poisson structure and the Birkhoff decomposition of U/K. This is done through reinterpretation of results of Pickrell. Each symplectic leaf admits a natural torus action. It is shown that these actions are Hamiltonian and the momentum maps are computed using triangular factorization. Finally, local formulas for the Evens-Lu Poisson structure are displayed in several examples.

In this thesis we seek exact solutions to the isotropic Einstien-Maxwell system that model the interior of relativistic stars. The field equations are transformed to a simpler form using the transformation of Durgapal and Bannerji (1983); the integration of the system is reduced to solving the condition of pressure isotropy. This condition is a recurrence relation with variable rational coe±cients which can be solved in general. New classes of solutions of linearly independent functions are obtained in terms of special functions and elementary functions for different spatial geometries. Our results contain models found previously including the superdense Tikekar (1990) neutron star model, the uncharged isotropic Maharaj and Leach (1996) solutions, the Finch and Skea (1989) model and the Durgapal and Bannerji (1983) superdense neutron star. Our general class of solutions also contain charged relativistic spheres found previously, including the model of Hansraj and Maharaj (2006) and the model of Thirukkanesh and Maharaj (2006). In addition, two exact analytical solutions describing the interior of a charged strange quark star are obtained by applying the MIT bag equation of state. We regain the Mak and Harko (2004) solution for a charged quark star as a special case. / Thesis (Ph. D.) University of KwaZulu-Natal, Westville, 2007.

Thesis (Ph.D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 50-53) Also available in print.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2000. / Includes bibliographical references (p. 41-42).