Sectional Curvature And Constantly Curved Spaces

The thesis investigates the sectional curvatures of four manifolds and some properties of constantly curved spaces. It is composed of three parts.In Chapter I, the motivations of our work are introduced. In addition, some preliminary concepts and lemmas are presented.In Chapter II, the concepts and characteristics of sectional curvatures from four manifolds such as Riemann manifold, Finsler manifold, Hesse manifold and Lorentz manifold are discussed. Moreover, some results from Rimann manifold are extended to the Lorentz manifold.In Chapter III, The properties of four constantly curved spaces in-cluding the Spheric surface, Hyperbolic space, Desitter space and Anti-de sitter space are analyzed respectively. Furthermore, we demonstrate that the sectional curvature in the four constantly curved spaces is a constant value.