Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 107-108).

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 107-108).

Wong, Yat Sen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 71-72). / Abstract also in Chinese. / Chapter 1 --- Lorentz Manifolds --- p.6 / Chapter 1.1 --- Preliminaries --- p.6 / Chapter 1.2 --- "Parallel Translation, geodesics and exponential map" --- p.9 / Chapter 1.3 --- "Curvature, frame field and Ricci curvature" --- p.14 / Chapter 1.4 --- Two-parameter maps --- p.15 / Chapter 2 --- Causal character in Lorentz geometry --- p.17 / Chapter 2.1 --- The Gauss Lemma --- p.17 / Chapter 2.2 --- Local causal character --- p.19 / Chapter 2.3 --- Timecones --- p.20 / Chapter 2.4 --- Local Lorentz Geometry --- p.21 / Chapter 3 --- Calculus of variations --- p.24 / Chapter 3.1 --- Jacobi fields --- p.24 / Chapter 3.2 --- Lorentz submanifolds --- p.25 / Chapter 3.3 --- The endmanifold case --- p.26 / Chapter 3.4 --- Focal points --- p.27 / Chapter 3.5 --- A causality theorem --- p.28 / Chapter 4 --- Causality in Lorentz manifolds --- p.32 / Chapter 4.1 --- Causality relations --- p.32 / Chapter 4.2 --- Quasi-limits --- p.35 / Chapter 4.3 --- Causality conditions --- p.37 / Chapter 4.4 --- Time separation --- p.39 / Chapter 4.5 --- Achronal sets --- p.42 / Chapter 4.6 --- Cauchy hypersurfaces --- p.43 / Chapter 4.7 --- Cauchy developments --- p.45 / Chapter 4.8 --- Spacelike hypersurfaces --- p.49 / Chapter 4.9 --- Cauchy horizons --- p.52 / Chapter 4.10 --- Hawking´ةs Singularity Theorem --- p.56 / Chapter 4.11 --- Penrose´ةs Singularity Theorem --- p.58 / Chapter 5 --- "Monge-Ampere equations, the Bergman kernel, and geometry of pesudoconvex domains" --- p.62 / Chapter 5.1 --- Monge-Ampere equations --- p.62 / Chapter 5.2 --- Differential geometry on the boundary --- p.63 / Chapter 5.3 --- Computations --- p.66 / Bibliography --- p.71

No description available.

A nonlinear wave equation invariant with respect to unitary representations of the Lorentz group is considered in an attempt to describe extended particles with spin and positive definite energy by means of a self-confined classical field. The wave function has an infinite number of components and, in the specific representations used, the corresponding internal degree of freedom is identified with the spin. A fractional power of the scalar bilinear invariant appears as an appropriate choice for the nonlinearity in order that all the stationary states be localized. Two approximation methods are proposed and both lead to results that bear a resemblance to the results of the MIT bag model.

Thesis (Ph. D.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves 172-175). Also available on the World Wide Web.