by Yiu Chun Chit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 81-82). / Chapter 1 --- Introduction --- p.7 / Chapter 1.1 --- Riemannian Manifolds --- p.7 / Chapter 1.1.1 --- Completeness --- p.8 / Chapter 1.1.2 --- Curvature tensor --- p.9 / Chapter 1.1.3 --- Holonomy --- p.11 / Chapter 1.2 --- Simply-connected Manifold of Nonpositive Sectional Curvature --- p.11 / Chapter 1.2.1 --- Topological structure --- p.12 / Chapter 1.2.2 --- Basic geometric properties --- p.13 / Chapter 1.2.3 --- Examples of nonpositively curved manifold --- p.20 / Chapter 1.2.4 --- Convexity properties --- p.23 / Chapter 1.2.5 --- Points at infinity for M --- p.27 / Chapter 2 --- Symmetric Spaces --- p.36 / Chapter 2.1 --- Symmetric Spaces of Noncompact Type --- p.36 / Chapter 2.1.1 --- Symmetric diffeomorphisms --- p.36 / Chapter 2.1.2 --- Transvections in I(M) --- p.38 / Chapter 2.1.3 --- Symmetric spaces as coset manifolds G/K --- p.39 / Chapter 2.1.4 --- Metric on TpM and the adjoint representation of Lie group --- p.41 / Chapter 2.1.5 --- Curvature tensor of M --- p.43 / Chapter 2.1.6 --- Killing form and classification of symmetric spaces --- p.44 / Chapter 2.1.7 --- Holonomy of M at p --- p.44 / Chapter 2.1.8 --- Rank of a symmetric space M --- p.45 / Chapter 2.1.9 --- Regular and singular points at infinity --- p.46 / Chapter 2.2 --- "The Symmetric Space Mn = SL(n,R)/SO(n,R)" --- p.46 / Chapter 2.2.1 --- Metric on TIMn --- p.47 / Chapter 2.2.2 --- Geodesic and symmetries of Mn --- p.48 / Chapter 2.2.3 --- Curvature of Mn --- p.48 / Chapter 2.2.4 --- Rank and flats in Mn --- p.49 / Chapter 2.2.5 --- Holonomy of Mn at I --- p.49 / Chapter 2.2.6 --- Eigenvalue-flag pair for a point in Mn(∞ ) --- p.50 / Chapter 2.2.7 --- Action of I0(Mn) on Mn(∞ ) --- p.52 / Chapter 2.2.8 --- Flags in opposition --- p.53 / Chapter 2.2.9 --- Joining points at infinity --- p.53 / Chapter 3 --- Group Action --- p.56 / Chapter 3.1 --- Action of Isometries on M(oo) --- p.56 / Chapter 3.1.1 --- Fundamental group as a group of isometries --- p.56 / Chapter 3.1.2 --- Lattices --- p.58 / Chapter 3.1.3 --- Duality condition --- p.59 / Chapter 3.1.4 --- Geodesic flows --- p.61 / Chapter 3.2 --- Action of Geodesic Symmetries on M(oo) --- p.62 / Chapter 3.3 --- Rank --- p.66 / Chapter 3.3.1 --- Rank of a manifold of nonpositive curvature --- p.66 / Chapter 3.3.2 --- Rank of the fundamental group --- p.68 / Chapter 3.4 --- Rigidity Theorems of Locally Symmetric Spaces --- p.69
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322009 |
| Date | January 1997 |
| Contributors | Yiu, Chun Chit., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 82 leaves : ill. ; 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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