Comparison Theorems in Riemannian Geometry. Dieser Artikel ist nicht verfügbar.Comparison Theorems in Riemannian Geometry

This item is printed on demand - Print on Demand Titel. Neuware -The main subject of this work are results of global Riemannian geometry. In all of these theorems we assume some local property of the space (usually formulated using curvature assumption) to derive some information about the global structure of the space, including the topological type of the manifold. In the first part of the work, we study the Bonnet-Myers theorem, the Rauch comparison theorem and the Cartan-Hadamard theorem. The second part is devoted to the sphere theorem, which was proven by Berger and Klingenberg. After extensive preparations, we give a complete proof of the theorem. Finally, we briefly discuss some recent developments that build on the sphere theorem.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 96 pp. Englisch.