The Foundations of Differential Geometry

by Oswald Veblen, J. H. C. Whitehead

Overview

This book contains a set of axioms for differential geometry and develops their consequences up to a point where a more advanced book might reasonably begin. Analytical operations with co-ordinate systems are continually used in differential geometry, a typical process being to 'choose a co-ordinate system such that …' It is therefore natural to state the axioms in terms of an undefined class of 'allowable' co-ordinate systems, and to deduce the properties of the space from the nature of the transformations of co-ordinates permitted by the axioms. These earlier axioms are found to be adequate for the differential geometry of an open simply connected space, the most elementary theorems of which occupy the greater part of Chapters III–V. The more general axioms, in terms of allowable co-ordinate systems and without restrictions on the connectivity of the space, are given in Chapter IV.

Product Details

ISBN-13:	9780521066747
Publisher:	Cambridge University Press
Publication date:	01/03/1932
Series:	Cambridge Tracts in Mathematics (Paperback)
Pages:	108
Product dimensions:	5.51(w) x 8.50(h) x 0.28(d)

Table of Contents

Preface; 1. The arithmetic space of n dimensions; 2. Geometries, groups and co-ordinate systems; 3. Allowable co-ordinates; 4. Cells and scalars; 5. Tangent spaces; 6. A set of axioms for differential geometry; 7. Various Geometries; Index of definitions.