Metric Foliations and Curvature (Progress in Mathematics) 〈Vol. 268〉

Gromoll, D./ Walschap, G.

Birkhäuser（2008/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 200 p.
• 商品コード 9783764387143

基本説明

Studies the main tool that is used for creating spaces of positive or nonnegative curvature.

Full Description

In the past three or four decades, there has been increasing realization that metric foliations play a key role in understanding the structure of Riemannian manifolds, particularly those with positive or nonnegative sectional curvature. In fact, all known such spaces are constructed from only a representative handful by means of metric fibrations or deformations thereof.

This text is an attempt to document some of these constructions, many of which have only appeared in journal form. The emphasis here is less on the fibration itself and more on how to use it to either construct or understand a metric with curvature of fixed sign on a given space.

Contents

Submersions, Foliations, and Metrics.- Basic Constructions and Examples.- Open Manifolds of Nonnegative Curvature.- Metric Foliations in Space Forms.