In this thesis, we will first extend the pseudo-locality of the Ricci flow on compact Riemannian manifolds discovered by Perelman to complete noncompact Riemannian manifolds. Then, we will apply it to study the long time existence of the Kahler-Ricci flow on complete noncompact Kahler manifolds with reasonable geometric assumptions. Finally, we will give some examples of complete flat Kahler metrics on the complex projective space with some divisor deleted. / by Yu, Chengjie. / Advisers: Yau-Heng Wan; Luen-Fai Tam. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3552. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 113-116). / 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.

by Fan Xuqian. / "August 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 84-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

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

"Submitted September 2002 ... Amended September 2004." / Bibliography: p. 152-157. / xvi, 157 p. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, School of Mathematical Sciences, Discipline of Pure Mathematics, 2004

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Computer Science." Includes bibliographical references (p. 143-154).

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Carmen Chicone. Vita. Includes bibliographical references.

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.

Bibliography: leaves 103-105. / xii, 105 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1997

Thesis (Ph.D.)--University of Adelaide, School of Mathematical Sciences, Discipline of Pure Mathematics, 2004. / "Submitted September 2002 ... Amended September 2004." Bibliography: p. 152-157.

Thesis (doctoral)--Universität Bonn, 1993. / Includes bibliographical references (p. 80-82).