The Foundations of Differential Geometry

Oswald Veblen, J. H. C. Whitehead

ISBN 10: 0521066743 / ISBN 13: 9780521066747

Published by Cambridge University Press, GB, 1932

About this Item

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.

Seller Inventory # LU-9780521066747

Bibliographic Details

• Title: The Foundations of Differential Geometry
• Publisher: Cambridge University Press, GB
• Publication Date: 1932
• Language: English
• ISBN 10: 0521066743
• ISBN 13: 9780521066747
• Binding: Paperback
• Condition: New
• Weight: 150 grams

About this title

Synopsis

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.

Book Description

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.