Geometry IV
Subtitle: Non-regular Riemannian Geometry
Publisher: Springer; Springer Berlin Heidelberg
Published: Dec 01, 2010
Format: paperback
Number of pages: 259
ISBN-13: 9783642081255
Description: This volume of the Encyclopaedia contains two articles, which give a survey of modern research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians. The first article written by Reshetnyak is devoted to the theory of two-dimensional Riemannian manifolds of bounded curvature. Concepts of Riemannian geometry, such as the area andintegral curvature of a set, and the length and integral curvature of a curve are also defined for these manifolds. Some fundamental results of Riemannian goemetry like the Gauss-Bonnet formula are true in the more general case considered in the book. The second article by Berestovskij and Nikolaev is devoted to the theory of metric spaces whose curvature lies between two given constants. The main result is that these spaces are infact Riemannian. This result has important applications in global Riemanniangeometry. Both parts cover topics, which have not yet been treated in monograph form. Hence the book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry.
Notes: Source title: Geometry IV: Non-regular Riemannian Geometry (Encyclopaedia of Mathematical Sciences (70))