Cheung, Yat Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 75-78). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Symplectic Geometry and Special Lagrangian Graphs in Cn --- p.10 / Chapter 2.1 --- Symplectic and Lagrangian Geometry of Cn --- p.10 / Chapter 2.2 --- Calibrated and Spccial Lagrangian Geometries in Cn --- p.13 / Chapter 2.3 --- Special Lagrangian Differential Equation --- p.16 / Chapter 3 --- Contact Geometry in S2n-1 --- p.20 / Chapter 3.1 --- Contact and Legendrian Geometries in S2n-1 --- p.20 / Chapter 3.2 --- Special Lagrangian Cone in R2n --- p.24 / Chapter 3.3 --- The Second Fundamental Form of Lagrangian Cone in E2n --- p.26 / Chapter 4 --- Geometry of Grassmannians --- p.29 / Chapter 4.1 --- Locally Symmetric Space --- p.29 / Chapter 4.2 --- "The Grassmann manifold G(n, m)" --- p.33 / Chapter 4.3 --- "Leichtweiss' Formula for Curvature Tensor in G(n, m)" --- p.36 / Chapter 4.4 --- "Normal Neighbourhoods of a Point in G(n, m)" --- p.39 / Chapter 4.5 --- Some Remarks on Lagrangian Grassmannians --- p.49 / Chapter 5 --- Harmonic Maps between Riemannian Manifolds --- p.51 / Chapter 5.1 --- Energy Functional and Tension Field --- p.52 / Chapter 5.2 --- Harmonic Map and Euler-Lagrange Equation --- p.56 / Chapter 5.3 --- The Gauss Map and its Tension Field --- p.59 / Chapter 5.4 --- Simple Riemannian Manifolds and A Liouville-Type Result of Har- monic Maps --- p.63 / Chapter 6 --- Bernstein-Type Results for Special Lagrangian Graphs --- p.65 / Chapter 6.1 --- Convexity and Bounded Slope Assumption --- p.65 / Chapter 6.2 --- Spherical Bernstein-Type Result --- p.68 / Chapter 6.3 --- Bernstein-Type Result with only Bounded Slope --- p.72 / Bibliography --- p.75
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327215 |
| Date | January 2010 |
| Contributors | Cheung, Yat Ming., 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, 78 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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