Leung, Wai Sing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-62). / Abstracts in English and Chinese. / Chapter 0.1 --- Introduction --- p.6 / Chapter 1 --- Sphere Theorems --- p.8 / Chapter 1.1 --- Rauch-Berger-Klingenberg Sphere Theorem --- p.8 / Chapter 1.2 --- Maximal Diameter Theorem --- p.15 / Chapter 1.3 --- Minimal Diameter Theorem --- p.17 / Chapter 2 --- A Differentiable Sphere Theorem --- p.27 / Chapter 2.1 --- Definitions --- p.27 / Chapter 2.2 --- Preliminary results not related to curvature --- p.28 / Chapter 2.3 --- Preliminary result related to the curvature --- p.33 / Chapter 2.4 --- Differentiable Sphere Theorem --- p.35 / Chapter 3 --- The fundamental equations of Riemannian submer- sions --- p.43 / Chapter 3.1 --- Definitions --- p.43 / Chapter 3.2 --- The fundamental tensors T and A --- p.44 / Chapter 3.3 --- Covariant derivatives of T and A --- p.47 / Chapter 3.4 --- Fundamental equations and O'Neill's formulas --- p.49 / Chapter 4 --- A study on exotic spheres --- p.52 / Chapter 4.1 --- Construction of Milnor sphere --- p.52 / Chapter 4.2 --- Construction of GM-sphere (Σ7) --- p.53 / Chapter 4.3 --- The curvature of Σ7 --- p.54 / Chapter 4.4 --- Some recent results and open questions --- p.59 / Bibliography --- p.61
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327186 |
| Date | January 2010 |
| Contributors | Leung, Wai Sing., 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, 1, 62 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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