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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327173 |
| Date | January 2010 |
| Contributors | Chen, Yunxia., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 56 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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