A study on sphere theorems and the curvature on exotic spheres.

• Other Authors: Leung, Wai Sing.
• Format: Others
• Language: English; Chinese
• Published: 2010
• Subjects: Sphere; Riemannian manifolds; Curves on surfaces
• Online Access: http://library.cuhk.edu.hk/record=b5894436; http://repository.lib.cuhk.edu.hk/en/item/cuhk-327186

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