Chao, Khek Lun Harold. / On t.p. "n" is superscript. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 67-68). / Abstracts in English and Chinese. / Chapter 1 --- Overview --- p.6 / Chapter 1.1 --- Introduction --- p.6 / Chapter 1.2 --- Domain of holomorphy --- p.7 / Chapter 1.3 --- Strongly pseudoconvex domains --- p.7 / Chapter 1.4 --- Geometry on the boundary --- p.10 / Chapter 1.5 --- Geometry in the interior --- p.12 / Chapter 1.6 --- Outline of the thesis --- p.13 / Chapter 2 --- Kahler-Einstein metric --- p.14 / Chapter 2.1 --- Problem --- p.14 / Chapter 2.2 --- Analysis of the domain --- p.15 / Chapter 2.3 --- Proof of openness --- p.23 / Chapter 2.4 --- Proof of closedness --- p.25 / Chapter 2.5 --- Uniqueness of solution --- p.33 / Chapter 2.6 --- Boundary behavior of the metric --- p.36 / Chapter 3 --- Boundary geometry of pseudo convex domains --- p.45 / Chapter 3.1 --- Background --- p.45 / Chapter 3.2 --- Monge-Ampere equation --- p.46 / Chapter 3.3 --- Differential geometry on the boundary --- p.51 / Chapter 3.4 --- Explicit calculation of the metric --- p.54 / Chapter 3.5 --- An example of spiralling chains --- p.63 / Bibliography --- p.67

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 66-68).

Geometric quantization is a subject of finding irreducible representations of certain group or algebra and identifying those equivalent representations by geometric means. Geometric quantization of even dimensional fermionic system has been constructed based on the spinor representation of even dimensional Clifford algebras. Although geometric quantization of odd dimensional fermionic system has not been done, the existence of spinor representations in odd dimension indicates that the geometric quantization is possible. In quantum field theory, charge conjungation can be defined on complex bosons and fermions. Without interaction, the particles and anti-particles essentially have same physical properties. In this thesis, we will first recall the setup of geometric quantization of even dimensional fermion and bosons. Then we will show how to quantize odd dimensional fermion. After that, charge conjungation on complex fermion and boson will be defined and the remaining effort will be put on how to identify the Hilbert spaces produced by different charge conjungations. / published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

No description available.

The holonomy group arising from a linear connection and differential homotopy is a classical subject in geometry. The notion was generalized first by Y. Muto ({10}) by considering horizontal subspaces in a fibred space which by construction is a differential manifold over a base space with another manifold as the fibre. He called this generalized group the restricted holonomy group Hl('o)((')M). Unlike the case of frame bundles the horizontal subspaces in a fibred space do not in general obey the right invariant rule. Hence it is not hard to imagine that Hl('o)((')M) is larger than linear holonomy groups. It may not even form a Lie group and for years the structure of this group was left unknown simply because the number of elements concerned is too large to handle. / One of the intentions here is to clarify and determine the structure of Hl('o)((')M) by setting certain conditions. Then by use of Palais' theorem about transformation groups, Nijenhuis' method for dealing with linear holonomy groups, and the standard technique of computing line integrals, the structure of Hl('o)((')M) is determined in Chapter One under certain conditions. Some properties concerning the isometric immersion from one fibred Riemannian space into another are also discussed in Chapter Two. / As far as I know, the work in this thesis is original, except where the text indicates the contrary: In particular, Chapter One is purely expository.

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (p. 159-170) Also available in print.

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 66-68).

Thèse--Paris. / Bibliography: p. 110-112.

Thèse--Paris. / Bibliography: p. 110-112.