O'Reilly logo

The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

V.23 Mostow’s Strong Rigidity Theorem

David Fisher

1 What Are Rigidity Theorems?

A typical rigidity theorem is a statement that some class of objects is much smaller than one might expect. To make this notion clear, let us look at some examples of MODULI SPACES [IV.8] that might lead us to expect that spaces of a certain type would in general be large.

2 Some Moduli Spaces

A flat metric on an n-dimensional MANIFOLD [I.3 §6.9] is a METRIC [III.56] that is locally isometric to the usual metric on the Euclidean space Imagen. In other words, every point x in the manifold is contained in a neighborhood Nx such that there is a distance-preserving bijection ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required