What is … the Nash embedding theorem?

This page hosts information on Ariane Beier's talk "What is … the Nash embedding theorem?" at the "What is …?" seminar. The talk will take place on Friday, May 3, 1:00pm at the BMS Loft at Urania. This talk will help you better understand the talk by László Székelyhidi, which will start at 2pm.

Abstract

The notion of a Riemannian manifold evolved from more concrete objects like surfaces in three-dimensional Euclidean space. But how much more general is this concept?

Nash's embedding theorem gives one answer to the question whether or not a Riemannian manifold can be isometrically embedded into Euclidean space. It provides surprising and, at first glance, inconsistent results which we want to illustrate by considering the example of a flat torus.

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