Ricci Curvature, Fundamental Groups and Rigidity

Autor:	CHEN, WEN-HAW, 陳文豪
Rok vydání:	1998
Druh dokumentu:	學位論文 ; thesis
Popis:	86 In this dissertation, we consider a class of closed Riemannian manifolds with lower Ricci curvature bound, upper diameter bound and almost maximal volume and show that the isomorphism types of fundamental groups characterize the diffeomorphism types of manifolds in such a class. The main tools are the Ricci curvature comparison arguments and the warped product spaces approximations. In particular, our result can be viewed as generalizationsof the well-known Mostow''s rigidity theorem and Cheeger''s finitenesstheorem. We also consider finite groups acting effectively on a compact negativelycurved manifold and show that there is at least one orbit with big diameter.It can also be regarded as a rigidity result for the finite exetensions offundamental groups of compact negatively curved manifolds.
Databáze:	Networked Digital Library of Theses & Dissertations
Externí odkaz:	http://ndltd.ncl.edu.tw/handle/86006603938472605341 Zobrazit plný text záznamu